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

3 <p>The LCM or Least Common Multiple of numbers is the smallest number which can be exactly divisible by each of the numbers. It can also be defined as the least common number, which is a common multiple of the numbers given. LCM helps in scheduling and coordinating prices, events, also used for revising timetables, etc.</p>

4 <h2>How to find the LCM of 30 and 50</h2>

5 <p>To find the LCM of 30 and 50 we will learn some methods: </p>

6 <ul><li>Listing Method</li>

7 </ul><ul><li>Prime Factorization Method</li>

8 </ul><ul><li>Division Method </li>

9 </ul><h3>LCM of 30 and 50 Using Listing the Multiples</h3>

10 <p>The Listing Multiples method is one of the methods used to find LCM of some given<a>numbers</a>. We have to know the<a>multiples</a>of the given numbers and then apply this method.</p>

11 <p><strong>Step 1: </strong>List down the multiples of each number</p>

12 <p> Multiples of 30 = 30,60,90,120,150,180,210,240,270,300,...</p>

13 <p> Multiples of 50= 50,100,150,200,250,300,350,400,450,500,...</p>

14 <p><strong>Step 2:</strong>Find out the smallest multiple from the listed multiples</p>

15 <p>The smallest<a>common multiple</a>is 150</p>

16 <p>Thus, LCM (30,50) = 150. </p>

17 <h3>LCM of 30 and 50 Using Prime Factorization</h3>

18 <p>Rule: The<a>prime factorization</a>of each number is to be done, and then the highest<a>power</a>of the prime<a>factors</a>are multiplied to get the LCM.</p>

19 <p><strong>Step 1: </strong>Find the prime factorization of the numbers:</p>

20 <p> Prime factorization of 30 = 3×2×5</p>

21 <p> Prime factorization of 50 = 52×2</p>

22 <p><strong>Step 2:</strong>Take the highest powers of each prime factor, and multiply the highest powers to get the LCM</p>

23 <p> 52×2×3 = 150</p>

24 <p> LCM (30,50) = 150. </p>

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27 <h3>LCM of 30 and 50 Using Division Method</h3>

26 <h3>LCM of 30 and 50 Using Division Method</h3>

28 <p>This is the most used method to find any LCM. It involves dividing both numbers 30 and 50 by their common prime factors until no further<a>division</a>is possible, then multiplying the divisors to find the LCM.</p>

27 <p>This is the most used method to find any LCM. It involves dividing both numbers 30 and 50 by their common prime factors until no further<a>division</a>is possible, then multiplying the divisors to find the LCM.</p>

29 <p><strong>Step 1:</strong>Write the numbers, divide by common prime factors. 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</p>

28 <p><strong>Step 1:</strong>Write the numbers, divide by common prime factors. 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</p>

30 <p>The first common prime divisors for both 30 and 50 are 2 or 5. We choose 5.</p>

29 <p>The first common prime divisors for both 30 and 50 are 2 or 5. We choose 5.</p>

31 <p><strong>Step 2:</strong>Dividing 30 and 50 with 5, we get 6 and 10 respectively.</p>

30 <p><strong>Step 2:</strong>Dividing 30 and 50 with 5, we get 6 and 10 respectively.</p>

32 <p><strong>Step 3:</strong>Repeat Step 1 and 2 till both are getting perfectly divided. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen<a>prime number</a>.</p>

31 <p><strong>Step 3:</strong>Repeat Step 1 and 2 till both are getting perfectly divided. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen<a>prime number</a>.</p>

33 <p>5×2×3×5 = 150</p>

32 <p>5×2×3×5 = 150</p>

34 <p>Thus, LCM (30,50) = 150 </p>

33 <p>Thus, LCM (30,50) = 150 </p>

35 <h2>Common Mistakes and How to Avoid Them in LCM of 30 and 50</h2>

34 <h2>Common Mistakes and How to Avoid Them in LCM of 30 and 50</h2>

36 <p>Misconception is normal, but we should avoid it whenever we are solving math problems. Let us see how we can avoid some common errors.</p>

35 <p>Misconception is normal, but we should avoid it whenever we are solving math problems. Let us see how we can avoid some common errors.</p>

37 <h3>Problem 1</h3>

36 <h3>Problem 1</h3>

38 <p>The LCM of 30 and 50 is 150. Then what will be the LCM of 40 and 50?</p>

37 <p>The LCM of 30 and 50 is 150. Then what will be the LCM of 40 and 50?</p>

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

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

40 <p> Prime Factorization of 40 =23×5</p>

39 <p> Prime Factorization of 40 =23×5</p>

41 <p>Prime factorization of 50 = 52×2</p>

40 <p>Prime factorization of 50 = 52×2</p>

42 <p>LCM(40,50)= 23×52 =200 </p>

41 <p>LCM(40,50)= 23×52 =200 </p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p> Solved the LCM of 40 and 50 through Prime Factorization method. </p>

43 <p> Solved the LCM of 40 and 50 through Prime Factorization method. </p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>LCM (30,50) = x. Find the smallest positive integer (n), where n×x=300 and the smallest positive integer (m), m× x=450</p>

46 <p>LCM (30,50) = x. Find the smallest positive integer (n), where n×x=300 and the smallest positive integer (m), m× x=450</p>

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

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

49 <p>LCM (30,50) = x </p>

48 <p>LCM (30,50) = x </p>

50 <p>We know that the LCM of 30 and 50 from the previous calculations. </p>

49 <p>We know that the LCM of 30 and 50 from the previous calculations. </p>

51 <p>LCM (30,50) = 150</p>

50 <p>LCM (30,50) = 150</p>

52 <p>n×150=300</p>

51 <p>n×150=300</p>

53 <p>⇒ n=300 /150</p>

52 <p>⇒ n=300 /150</p>

54 <p>⇒ n = 2</p>

53 <p>⇒ n = 2</p>

55 <p>Similarly, </p>

54 <p>Similarly, </p>

56 <p>LCM (30,50) = 150</p>

55 <p>LCM (30,50) = 150</p>

57 <p>n×150=450</p>

56 <p>n×150=450</p>

58 <p>⇒ n=450 /150</p>

57 <p>⇒ n=450 /150</p>

59 <p>⇒ n = 3</p>

58 <p>⇒ n = 3</p>

60 <p>Answer: 2, 3. </p>

59 <p>Answer: 2, 3. </p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <p>We made use of the LCM of 30 and 50 and solved the equation to get the value of n in both the problems.</p>

61 <p>We made use of the LCM of 30 and 50 and solved the equation to get the value of n in both the problems.</p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h3>Problem 3</h3>

63 <h3>Problem 3</h3>

65 <p>What is the LCM of 30, 50 and 60?</p>

64 <p>What is the LCM of 30, 50 and 60?</p>

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

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

67 <p> Prime factorization of 30 = 3×2×5</p>

66 <p> Prime factorization of 30 = 3×2×5</p>

68 <p>Prime factorization of 50 = 52×2</p>

67 <p>Prime factorization of 50 = 52×2</p>

69 <p>Prime Factorization of 60 =22×3×5</p>

68 <p>Prime Factorization of 60 =22×3×5</p>

70 <p>LCM (30,50,60)= 22×3×52 =300</p>

69 <p>LCM (30,50,60)= 22×3×52 =300</p>

71 <p>Answer: 300 </p>

70 <p>Answer: 300 </p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p> The LCM of numbers 30,50 and 60 are found using the Prime factorization method. </p>

72 <p> The LCM of numbers 30,50 and 60 are found using the Prime factorization method. </p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h2>FAQs on LCM of 30 and 50</h2>

74 <h2>FAQs on LCM of 30 and 50</h2>

76 <h3>1.What is the GCF of 30 and 50?</h3>

75 <h3>1.What is the GCF of 30 and 50?</h3>

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

76 <p>Factors of 30: 1,2,3,5,6,10,15,30.</p>

78 <p>Factors of 50: 1,2,5,10,25,50.</p>

77 <p>Factors of 50: 1,2,5,10,25,50.</p>

79 <p>Common factors of 30 and 50: 1,2,5,10</p>

78 <p>Common factors of 30 and 50: 1,2,5,10</p>

80 <p>So, Highest<a>common factor</a>of 30 and 50: 10 </p>

79 <p>So, Highest<a>common factor</a>of 30 and 50: 10 </p>

81 <h3>2.What is the LCM of 25,30, and 50?</h3>

80 <h3>2.What is the LCM of 25,30, and 50?</h3>

82 <p> Prime factorization of 30 = 3×2×5</p>

81 <p> Prime factorization of 30 = 3×2×5</p>

83 <p>Prime factorization of 50 = 52×2</p>

82 <p>Prime factorization of 50 = 52×2</p>

84 <p>Prime Factorization of 25 =52</p>

83 <p>Prime Factorization of 25 =52</p>

85 <p>LCM (25,30,50) = 52×2×3 = 150 </p>

84 <p>LCM (25,30,50) = 52×2×3 = 150 </p>

86 <h3>3.What is the LCM of 30 and 53?</h3>

85 <h3>3.What is the LCM of 30 and 53?</h3>

87 <p> Prime factorization of 30 = 3×2×5</p>

86 <p> Prime factorization of 30 = 3×2×5</p>

88 <p>Prime Factorization of 53 = 53×1</p>

87 <p>Prime Factorization of 53 = 53×1</p>

89 <p>LCM (30,53) = 3×2×5×53 = 1590</p>

88 <p>LCM (30,53) = 3×2×5×53 = 1590</p>

90 <h3>4.What is the LCM of 30 and 60?</h3>

89 <h3>4.What is the LCM of 30 and 60?</h3>

91 <p>Prime factorization of 30 = 3×2×5</p>

90 <p>Prime factorization of 30 = 3×2×5</p>

92 <p>Prime factorization of 60 = 22×3×5</p>

91 <p>Prime factorization of 60 = 22×3×5</p>

93 <p>LCM (30,60) = 5×22×3 = 60 </p>

92 <p>LCM (30,60) = 5×22×3 = 60 </p>

94 <h3>5.What is the LCM of 35 and 50?</h3>

93 <h3>5.What is the LCM of 35 and 50?</h3>

95 <p> Prime factorization of 50 = 52×2</p>

94 <p> Prime factorization of 50 = 52×2</p>

96 <p>Prime Factorization of 35 =5×7</p>

95 <p>Prime Factorization of 35 =5×7</p>

97 <p>LCM (35,50) = 52×2×7 = 350 </p>

96 <p>LCM (35,50) = 52×2×7 = 350 </p>

98 <h2>Important glossaries for the LCM of 35 and 50</h2>

97 <h2>Important glossaries for the LCM of 35 and 50</h2>

99 <ul><li><strong>Prime Factor:</strong>A natural number or whole number which has factors that are 1 and itself.</li>

98 <ul><li><strong>Prime Factor:</strong>A natural number or whole number which has factors that are 1 and itself.</li>

100 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>

99 </ul><ul><li><strong>Prime Factorization:</strong>The process of breaking down a number into its prime factors is called Prime Factorization. </li>

101 </ul><ul><li><strong>Co-prime numbers:</strong>numbers which have the only positive divisor of them both as 1. </li>

100 </ul><ul><li><strong>Co-prime numbers:</strong>numbers which have the only positive divisor of them both as 1. </li>

102 </ul><ul><li><strong>HCF or GCF:</strong>GCF (Greatest common factor) is the largest factor that divides both numbers.</li>

101 </ul><ul><li><strong>HCF or GCF:</strong>GCF (Greatest common factor) is the largest factor that divides both numbers.</li>

103 </ul><ul><li><strong>Multiples:</strong>The product we get when all the integers are multiplied with a particular number, one by one.</li>

102 </ul><ul><li><strong>Multiples:</strong>The product we get when all the integers are multiplied with a particular number, one by one.</li>

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

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

105 <p>▶</p>

104 <p>▶</p>

106 <h2>Hiralee Lalitkumar Makwana</h2>

105 <h2>Hiralee Lalitkumar Makwana</h2>

107 <h3>About the Author</h3>

106 <h3>About the Author</h3>

108 <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>

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>

109 <h3>Fun Fact</h3>

108 <h3>Fun Fact</h3>

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

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