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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>In this article, we will learn how to learn LCM by using different methods and learn to apply the LCM. We can simplify mathematical calculations and efficiently solve the problems by learning the LCM</p>

4 <h2>What is the LCM of 30 and 42?</h2>

5 <h2>How to find the LCM of 30 and 42?</h2>

6 <p>We can find the LCM using the listing method,<a>prime factorization</a>method and<a>division</a>method as explained below; </p>

7 <h3>LCM of 30 and 42 using the Listing multiples method</h3>

8 <p>The LCM of 30 and 42 can be found using the following steps</p>

9 <p><strong>Step 1: </strong>Write down the multiples of each number: </p>

10 <p>Multiples of 30-30,60,90,120,150,180,210,…</p>

11 <p>Multiples of 42-42,84,126,168,210,…</p>

12 <p><strong>Step 2:</strong> Pick the smallest multiple from the multiples of 30 and 42. </p>

13 <p>The LCM of 30 and 42 = 210 </p>

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16 <h3>LCM of 30 and 42 using the Prime Factorization</h3>

15 <h3>LCM of 30 and 42 using the Prime Factorization</h3>

17 <p>The prime<a>factors</a>of the given numbers are written, and the highest<a>power</a>of the prime factors is multiplied to get the LCM.</p>

16 <p>The prime<a>factors</a>of the given numbers are written, and the highest<a>power</a>of the prime factors is multiplied to get the LCM.</p>

18 <p><strong>Step 1: </strong>Find the prime factors of the numbers:</p>

17 <p><strong>Step 1: </strong>Find the prime factors of the numbers:</p>

19 <p>30= 3×5×2</p>

18 <p>30= 3×5×2</p>

20 <p>42 = 2×3×7</p>

19 <p>42 = 2×3×7</p>

21 <p><strong>Step 2 : </strong>Multiply the highest power of each factor to get the LCM. </p>

20 <p><strong>Step 2 : </strong>Multiply the highest power of each factor to get the LCM. </p>

22 <p>LCM (30,42) = 210</p>

21 <p>LCM (30,42) = 210</p>

23 <h3>LCM of 30 and 42 using the Division Method</h3>

22 <h3>LCM of 30 and 42 using the Division Method</h3>

24 <p>The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. </p>

23 <p>The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. </p>

25 <p><strong>Step 1 : </strong>Write down the numbers in a row;</p>

24 <p><strong>Step 1 : </strong>Write down the numbers in a row;</p>

26 <p><strong>Step 2 :</strong>A prime<a>integer</a>that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’. Carry forward the numbers not divisible by the previously picked<a>prime number</a>.</p>

25 <p><strong>Step 2 :</strong>A prime<a>integer</a>that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’. Carry forward the numbers not divisible by the previously picked<a>prime number</a>.</p>

27 <p> <strong>Step 3 :</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e, LCM (30,42) = 210</p>

26 <p> <strong>Step 3 :</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e, LCM (30,42) = 210</p>

28 <h2>Common Mistakes and how to avoid them in LCM of 30 and 42</h2>

27 <h2>Common Mistakes and how to avoid them in LCM of 30 and 42</h2>

29 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 30 and 42 make a note while practicing. </p>

28 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 30 and 42 make a note while practicing. </p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>Verify LCM(a,b)×HCF(a,b)=a×b, where a= 30 and b=42.</p>

30 <p>Verify LCM(a,b)×HCF(a,b)=a×b, where a= 30 and b=42.</p>

32 <p>Okay, lets begin</p>

31 <p>Okay, lets begin</p>

33 <p>LCM of 30,42; </p>

32 <p>LCM of 30,42; </p>

34 <p>Prime factorize the numbers; </p>

33 <p>Prime factorize the numbers; </p>

35 <p>30= 3×5×2</p>

34 <p>30= 3×5×2</p>

36 <p>42 = 2×3×7</p>

35 <p>42 = 2×3×7</p>

37 <p>LCM (30,42) = 210</p>

36 <p>LCM (30,42) = 210</p>

38 <p>HCF of 30,42; </p>

37 <p>HCF of 30,42; </p>

39 <p>Factors of 30-1,2,3,5,6,10,15,30</p>

38 <p>Factors of 30-1,2,3,5,6,10,15,30</p>

40 <p>Factors of 42-1,2,3,6,7,21,42</p>

39 <p>Factors of 42-1,2,3,6,7,21,42</p>

41 <p>HCF(30,42)= 6</p>

40 <p>HCF(30,42)= 6</p>

42 <p>Verifying the formula; </p>

41 <p>Verifying the formula; </p>

43 <p>LCM(a,b)×HCF(a,b)=a×b</p>

42 <p>LCM(a,b)×HCF(a,b)=a×b</p>

44 <p>210×6=30×42</p>

43 <p>210×6=30×42</p>

45 <p>1260 =1260 </p>

44 <p>1260 =1260 </p>

46 <h3>Explanation</h3>

45 <h3>Explanation</h3>

47 <p>The LHS is equal to the RHS, hence the relationship as given in the formula stands true. </p>

46 <p>The LHS is equal to the RHS, hence the relationship as given in the formula stands true. </p>

48 <p>Well explained 👍</p>

47 <p>Well explained 👍</p>

49 <h3>Problem 2</h3>

48 <h3>Problem 2</h3>

50 <p>The LCM of 30 and x is 210. HCF of 30 and x is 6. Find x.</p>

49 <p>The LCM of 30 and x is 210. HCF of 30 and x is 6. Find x.</p>

51 <p>Okay, lets begin</p>

50 <p>Okay, lets begin</p>

52 <p>Given;</p>

51 <p>Given;</p>

53 <p>LCM(30,x) = 210</p>

52 <p>LCM(30,x) = 210</p>

54 <p>HCF(30,x) = 6 </p>

53 <p>HCF(30,x) = 6 </p>

55 <p>To find x, we use →LCM(a,b)=a×b/HCF(a,b) </p>

54 <p>To find x, we use →LCM(a,b)=a×b/HCF(a,b) </p>

56 <p>We now solve for x, </p>

55 <p>We now solve for x, </p>

57 <p>30×x/6 = 210 </p>

56 <p>30×x/6 = 210 </p>

58 <p>30×x = 210×6</p>

57 <p>30×x = 210×6</p>

59 <p>30×x = 1260 </p>

58 <p>30×x = 1260 </p>

60 <p>x = 1260/30 = 42 </p>

59 <p>x = 1260/30 = 42 </p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>The above is how we ascertain the value of x, which is 42. </p>

61 <p>The above is how we ascertain the value of x, which is 42. </p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>Find x where, LCM (32,x)=210 and HCF(32,x)=6.</p>

64 <p>Find x where, LCM (32,x)=210 and HCF(32,x)=6.</p>

66 <p>Okay, lets begin</p>

65 <p>Okay, lets begin</p>

67 <p>x= 40 </p>

66 <p>x= 40 </p>

68 <h3>Explanation</h3>

67 <h3>Explanation</h3>

69 <p>The only number that satisfies both the conditions LCM (32,x)=210 and HCF(32,x)=6 is 42. HCF of 30 and 42 is 6 and the LCM of the same is 210. </p>

68 <p>The only number that satisfies both the conditions LCM (32,x)=210 and HCF(32,x)=6 is 42. HCF of 30 and 42 is 6 and the LCM of the same is 210. </p>

70 <p>Well explained 👍</p>

69 <p>Well explained 👍</p>

71 <h2>FAQ’s on LCM of 30 and 42</h2>

70 <h2>FAQ’s on LCM of 30 and 42</h2>

72 <h3>1.What is the LCM of 35 and 42?</h3>

71 <h3>1.What is the LCM of 35 and 42?</h3>

73 <p>Prime factorize the numbers;</p>

72 <p>Prime factorize the numbers;</p>

74 <p>35 = 3×7</p>

73 <p>35 = 3×7</p>

75 <p>42 = 2×3×7</p>

74 <p>42 = 2×3×7</p>

76 <p>LCM (35,42) = 210 </p>

75 <p>LCM (35,42) = 210 </p>

77 <h3>2.What are the factors of 30 and 42?</h3>

76 <h3>2.What are the factors of 30 and 42?</h3>

78 <p>Factors of 30-1,2,3,5,6,10,15,30</p>

77 <p>Factors of 30-1,2,3,5,6,10,15,30</p>

79 <p>Factors of 42-1,2,3,6,7,21,42</p>

78 <p>Factors of 42-1,2,3,6,7,21,42</p>

80 <p>Common factors of 30 and 42-1,2,3,6 </p>

79 <p>Common factors of 30 and 42-1,2,3,6 </p>

81 <h3>3.What is the LCM of 26 and 39?</h3>

80 <h3>3.What is the LCM of 26 and 39?</h3>

82 <p>Prime factorize the numbers;</p>

81 <p>Prime factorize the numbers;</p>

83 <p>26 = 2×13</p>

82 <p>26 = 2×13</p>

84 <p>39 = 13×3</p>

83 <p>39 = 13×3</p>

85 <p>LCM(26,39) = 78 </p>

84 <p>LCM(26,39) = 78 </p>

86 <h3>4. What is the LCM of 30,42 and 48?</h3>

85 <h3>4. What is the LCM of 30,42 and 48?</h3>

87 <p>Prime factorize the numbers;</p>

86 <p>Prime factorize the numbers;</p>

88 <p>30 = 2×3×5</p>

87 <p>30 = 2×3×5</p>

89 <p> 42 = 2×3×7</p>

88 <p> 42 = 2×3×7</p>

90 <p>48 = 2×2×2×2×3</p>

89 <p>48 = 2×2×2×2×3</p>

91 <p>LCM (30,32,48) = 1680 </p>

90 <p>LCM (30,32,48) = 1680 </p>

92 <h3>5.What is the LCM of 30 and 48?</h3>

91 <h3>5.What is the LCM of 30 and 48?</h3>

93 <p>Prime factorize the numbers;</p>

92 <p>Prime factorize the numbers;</p>

94 <p>30 = 2×3×5</p>

93 <p>30 = 2×3×5</p>

95 <p>48 = 2×2×2×2×3</p>

94 <p>48 = 2×2×2×2×3</p>

96 <p>LCM(30,48) = 240 </p>

95 <p>LCM(30,48) = 240 </p>

97 <h2>Important glossaries for the LCM of 30 and 42</h2>

96 <h2>Important glossaries for the LCM of 30 and 42</h2>

98 <ul><li><strong>Multiple</strong>- It is a product of a number and any natural integer. So for 30,both 3,2 and 5 are the multiples.</li>

97 <ul><li><strong>Multiple</strong>- It is a product of a number and any natural integer. So for 30,both 3,2 and 5 are the multiples.</li>

99 </ul><ul><li><strong>Prime Factor</strong>- It is a prime number that one gets after factorization of any given number. Like for 30, 2,3,5,6,15 and 30 are prime factors as they can be divided by 1 or the number itself.</li>

98 </ul><ul><li><strong>Prime Factor</strong>- It is a prime number that one gets after factorization of any given number. Like for 30, 2,3,5,6,15 and 30 are prime factors as they can be divided by 1 or the number itself.</li>

100 </ul><ul><li><strong>Prime Factorization</strong>- It is a process of dividing the number into prime factors.</li>

99 </ul><ul><li><strong>Prime Factorization</strong>- It is a process of dividing the number into prime factors.</li>

101 </ul><ul><li><strong>Co-prime numbers</strong>- These are the positive integers where both the numbers can be divided only by 1. </li>

100 </ul><ul><li><strong>Co-prime numbers</strong>- These are the positive integers where both the numbers can be divided only by 1. </li>

102 </ul><ul><li><strong>Fraction</strong>- It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 30/5 ,30 is the numerator and 5 is the denominator. Proper fraction is where numerator is always lesser than denominator. </li>

101 </ul><ul><li><strong>Fraction</strong>- It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 30/5 ,30 is the numerator and 5 is the denominator. Proper fraction is where numerator is always lesser than denominator. </li>

103 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

102 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

104 <p>▶</p>

103 <p>▶</p>

105 <h2>Hiralee Lalitkumar Makwana</h2>

104 <h2>Hiralee Lalitkumar Makwana</h2>

106 <h3>About the Author</h3>

105 <h3>About the Author</h3>

107 <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>

106 <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>

108 <h3>Fun Fact</h3>

107 <h3>Fun Fact</h3>

109 <p>: She loves to read number jokes and games.</p>

108 <p>: She loves to read number jokes and games.</p>