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2026-01-01
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>LCM is the smallest and a common multiple of the numbers 120 and 150. We often apply the LCM to solve problems that have in them fractions, percentages, time intervals and others. Below, we explain how we find the LCM of 120 and 150.</p>
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<p>LCM is the smallest and a common multiple of the numbers 120 and 150. We often apply the LCM to solve problems that have in them fractions, percentages, time intervals and others. Below, we explain how we find the LCM of 120 and 150.</p>
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<h2>What is the LCM of 120 and 150?</h2>
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<h2>What is the LCM of 120 and 150?</h2>
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<h3>LCM of 120 and 150 Using Listing the Multiples</h3>
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<h3>LCM of 120 and 150 Using Listing the Multiples</h3>
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<p><strong>Step 1:</strong>List multiples of the<a>numbers</a>; </p>
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<p><strong>Step 1:</strong>List multiples of the<a>numbers</a>; </p>
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<p>120-120,240,360,480,600,…</p>
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<p>120-120,240,360,480,600,…</p>
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<p>150- 150,300,450,600,…</p>
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<p>150- 150,300,450,600,…</p>
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<p><strong>Step 2: </strong>Find the smallest common number </p>
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<p><strong>Step 2: </strong>Find the smallest common number </p>
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<p>LCM(120,150) = 600 </p>
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<p>LCM(120,150) = 600 </p>
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<h3>LCM of 120 and 150 Using Prime Factorization</h3>
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<h3>LCM of 120 and 150 Using Prime Factorization</h3>
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<p><strong>Step 1:</strong>Prime factorize the numbers </p>
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<p><strong>Step 1:</strong>Prime factorize the numbers </p>
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<p>120 = 2×2×2×3×5</p>
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<p>120 = 2×2×2×3×5</p>
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<p>150= 2×3×5×5</p>
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<p>150= 2×3×5×5</p>
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<p><strong>Step 2: </strong>Multiply highest<a>powers</a> </p>
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<p><strong>Step 2: </strong>Multiply highest<a>powers</a> </p>
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<p>23×3×52 = 600 </p>
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<p>23×3×52 = 600 </p>
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<p>LCM(120,150) = 600 </p>
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<p>LCM(120,150) = 600 </p>
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<h3>LCM of 120 and 150 Using Division Method</h3>
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<h3>LCM of 120 and 150 Using Division Method</h3>
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<ul><li>Write the numbers in a row </li>
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<ul><li>Write the numbers in a row </li>
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</ul><ul><li>Divide them by their common prime<a>factors</a> </li>
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</ul><ul><li>Divide them by their common prime<a>factors</a> </li>
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</ul><ul><li>Carry forward the numbers that are not divided by the previously chosen number</li>
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</ul><ul><li>Carry forward the numbers that are not divided by the previously chosen number</li>
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</ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>
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</ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>
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</ul><ul><li>Multiply the divisors to find the LCM - 2×2×2×3×5×5 = 600</li>
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</ul><ul><li>Multiply the divisors to find the LCM - 2×2×2×3×5×5 = 600</li>
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</ul><ul><li>LCM(120,150) = 600 </li>
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</ul><ul><li>LCM(120,150) = 600 </li>
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</ul><h2>Common mistakes to avoid while finding the LCM of 120 and 150</h2>
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</ul><h2>Common mistakes to avoid while finding the LCM of 120 and 150</h2>
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<p>Listed here are a few mistakes that are frequently made when trying to find the LCM. </p>
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<p>Listed here are a few mistakes that are frequently made when trying to find the LCM. </p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Two machines A and B complete a cycle in 120 and 150 minutes, respectively. After how many minutes will both machines complete their cycle together again?</p>
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<p>Two machines A and B complete a cycle in 120 and 150 minutes, respectively. After how many minutes will both machines complete their cycle together again?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The LCM(120, 150) = 600 minutes. </p>
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<p>The LCM(120, 150) = 600 minutes. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> Both machines will complete a cycle together in 600 minutes. </p>
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<p> Both machines will complete a cycle together in 600 minutes. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>The LCM of two numbers is 36 and the sum is 21. Find the numbers.</p>
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<p>The LCM of two numbers is 36 and the sum is 21. Find the numbers.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>LCM(a, b) = 36 </p>
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<p>LCM(a, b) = 36 </p>
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<p>a+b= 21</p>
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<p>a+b= 21</p>
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<p>We know that, LCM(a, b)×HCF(a, b) =a×b </p>
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<p>We know that, LCM(a, b)×HCF(a, b) =a×b </p>
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<p>Let us assume that the numbers a and b are 8 and 10, </p>
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<p>Let us assume that the numbers a and b are 8 and 10, </p>
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<p>8+10 = 18, it is not equal to the sum given</p>
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<p>8+10 = 18, it is not equal to the sum given</p>
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<p>Let us assume that the numbers a and b are 12 and 30,</p>
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<p>Let us assume that the numbers a and b are 12 and 30,</p>
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<p>30+12= 42, which is equal to the sum given</p>
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<p>30+12= 42, which is equal to the sum given</p>
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<p>Product of 12 and 30; </p>
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<p>Product of 12 and 30; </p>
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<p>30 ×12= 360</p>
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<p>30 ×12= 360</p>
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<p>LCM(a, b)×HCF(a, b) =a×b </p>
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<p>LCM(a, b)×HCF(a, b) =a×b </p>
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<p>LCM (30,12)×HCF(30,12) =30×12 </p>
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<p>LCM (30,12)×HCF(30,12) =30×12 </p>
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<p>LCM of 30,12; </p>
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<p>LCM of 30,12; </p>
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<p>Prime factorization of 12 = 2×2×3</p>
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<p>Prime factorization of 12 = 2×2×3</p>
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<p>Prime factorization of 30 = 5×2×3</p>
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<p>Prime factorization of 30 = 5×2×3</p>
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<p>LCM(30,12) = 60</p>
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<p>LCM(30,12) = 60</p>
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<p>HCF of 30,12; </p>
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<p>HCF of 30,12; </p>
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<p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>
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<p>Factors of 30 = 1,2,3,5,6,10,15,30 </p>
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<p>Factors of 12 = 1,2,3,4,6,12</p>
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<p>Factors of 12 = 1,2,3,4,6,12</p>
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<p>HCF(30,12) = 6</p>
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<p>HCF(30,12) = 6</p>
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<p>60×6 =30×12 </p>
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<p>60×6 =30×12 </p>
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<p>360 =360 </p>
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<p>360 =360 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> We, by assuming that a and b are 12 and 30 respectively and verifying the same against the formula figures that the assumption is right and a=12,b=30. </p>
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<p> We, by assuming that a and b are 12 and 30 respectively and verifying the same against the formula figures that the assumption is right and a=12,b=30. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>If 120 items represent 20% of a total, and 150 items represent 25% of another total, what is the least common multiple of the totals?</p>
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<p>If 120 items represent 20% of a total, and 150 items represent 25% of another total, what is the least common multiple of the totals?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>20% = 120 </p>
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<p>20% = 120 </p>
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<p>Total = 120/ 0.2 = 600</p>
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<p>Total = 120/ 0.2 = 600</p>
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<p>25% = 150 </p>
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<p>25% = 150 </p>
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<p>Total = 150/0.25 = 600 </p>
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<p>Total = 150/0.25 = 600 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Thus, the LCM of the totals is 600. </p>
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<p>Thus, the LCM of the totals is 600. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the LCM of 120 and 150</h2>
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<h2>FAQs on the LCM of 120 and 150</h2>
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<h3>1.What is the HCF of 120 and 150?</h3>
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<h3>1.What is the HCF of 120 and 150?</h3>
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<p>Factors of 120-1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 </p>
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<p>Factors of 120-1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 </p>
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<p>Factors of 150-1,2,3,5,6,10,15,25,30,50,75,150 </p>
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<p>Factors of 150-1,2,3,5,6,10,15,25,30,50,75,150 </p>
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<p>HCF(120,150) = 30 </p>
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<p>HCF(120,150) = 30 </p>
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<h3>2.What is the LCM of 125 and 150?</h3>
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<h3>2.What is the LCM of 125 and 150?</h3>
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<p>LCM(125,150) = 750. 750 is the smallest<a>common multiple</a>number of the numbers 125 and 150. </p>
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<p>LCM(125,150) = 750. 750 is the smallest<a>common multiple</a>number of the numbers 125 and 150. </p>
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<h3>3.What is the LCM of 100,150 and 120.</h3>
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<h3>3.What is the LCM of 100,150 and 120.</h3>
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<p>The smallest number and a common multiple of the numbers 100,150 and 120 is their LCM. LCM of 100,150 and 120 is 600. </p>
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<p>The smallest number and a common multiple of the numbers 100,150 and 120 is their LCM. LCM of 100,150 and 120 is 600. </p>
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<h3>4.What is the LCM of 45,120 and 150?</h3>
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<h3>4.What is the LCM of 45,120 and 150?</h3>
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<p>1800 is the LCM of 45,120 and 150. It is the smallest number and a common multiple of the numbers 45,12 and 150. </p>
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<p>1800 is the LCM of 45,120 and 150. It is the smallest number and a common multiple of the numbers 45,12 and 150. </p>
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<h3>5.What is the LCM of 150 and 225?</h3>
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<h3>5.What is the LCM of 150 and 225?</h3>
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<p>LCM of 150 and 225 = 450. 450 is the smallest multiple of 150 and 225. </p>
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<p>LCM of 150 and 225 = 450. 450 is the smallest multiple of 150 and 225. </p>
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<h2>Important glossaries for LCM of 120 and 150</h2>
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<h2>Important glossaries for LCM of 120 and 150</h2>
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<ul><li><strong>Multiple:</strong>product of a number and integer </li>
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<ul><li><strong>Multiple:</strong>product of a number and integer </li>
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</ul><ul><li><strong>Prime Factor:</strong>a number whose factors are itself and 1 </li>
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</ul><ul><li><strong>Prime Factor:</strong>a number whose factors are itself and 1 </li>
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</ul><ul><li><strong>Prime Factorization:</strong>breaking a large number into its prime factors </li>
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</ul><ul><li><strong>Prime Factorization:</strong>breaking a large number into its prime factors </li>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>▶</p>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h2>Hiralee Lalitkumar Makwana</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She loves to read number jokes and games.</p>
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<p>: She loves to read number jokes and games.</p>