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1 - <p>346 Learners</p>

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

3 <p>The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 25. LCM helps to solve problems with fractions and scenarios like setting an alarm or planning to align events.</p>

4 <h2>What is the LCM of 10 and 25?</h2>

5 <h2>How to find the LCM of 10 and 25 ?</h2>

6 <p>There are various methods to find the LCM, Listing method,<a>prime factorization</a>method and<a>division</a>method are explained below; </p>

7 <h3>LCM of 10 and 25 using the Listing multiples method</h3>

8 <p>To ascertain the LCM, list the multiples of the<a>integers</a>until a<a>common multiple</a>is found. </p>

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

10 <p>Multiples of 10 = 10,20,30,40,50,…</p>

11 <p>Multiples of 25 = 25,50,75,…</p>

12 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples of 10 and 25. </p>

13 <p>The LCM (Least common multiple) of 10 and 25 is 50.<a>i</a>.e., 50 is divisible by 10 and 25 with no reminder. </p>

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16 <h3>LCM of 10 and 25 using the Prime Factorization</h3>

15 <h3>LCM of 10 and 25 using the Prime Factorization</h3>

17 <p>This method involves finding the prime<a>factors</a>of each number and then multiplying the highest<a>power</a>of the prime factors to get the LCM.</p>

16 <p>This method involves finding the prime<a>factors</a>of each number and then multiplying the highest<a>power</a>of the prime factors 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>Prime factorization of 10 = 2×5</p>

18 <p>Prime factorization of 10 = 2×5</p>

20 <p>Prime factorization of 25 = 5×5</p>

19 <p>Prime factorization of 25 = 5×5</p>

21 <p> Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

20 <p> Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

22 <p>LCM (10,25) = 50</p>

21 <p>LCM (10,25) = 50</p>

23 <h3>LCM of 10 and 25 using the Division Method</h3>

22 <h3>LCM of 10 and 25 using the Division Method</h3>

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

23 <p>The Division Method involves 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>Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given numbers. </p>

25 <p> <strong>Step 2: </strong>Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given numbers. </p>

27 <p><strong>Step 3: </strong>Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.</p>

26 <p><strong>Step 3: </strong>Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.</p>

28 <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 (10,25) = 50</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 (10,25) = 50</p>

29 <h2>Common Mistakes and how to avoid them in LCM of 10 and 25</h2>

28 <h2>Common Mistakes and how to avoid them in LCM of 10 and 25</h2>

30 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 25, make a note while practicing. </p>

29 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 10 and 25, make a note while practicing. </p>

31 <h3>Problem 1</h3>

30 <h3>Problem 1</h3>

32 <p>The LCM of a and b is 50. Given a is 10, find b.</p>

31 <p>The LCM of a and b is 50. Given a is 10, find b.</p>

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

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

34 <p>Using the formula; </p>

33 <p>Using the formula; </p>

35 <p>LCM(a,b) =a×b/HCF(a,b) </p>

34 <p>LCM(a,b) =a×b/HCF(a,b) </p>

36 <p>a =10, b= ?</p>

35 <p>a =10, b= ?</p>

37 <p>LCM (a, b) = 50</p>

36 <p>LCM (a, b) = 50</p>

38 <p>The factors of 10 (a) are - 1,2,5,10; so we can assume that the HCF is one of these numbers.</p>

37 <p>The factors of 10 (a) are - 1,2,5,10; so we can assume that the HCF is one of these numbers.</p>

39 <p> By testing the values, we find the possible values of b. </p>

38 <p> By testing the values, we find the possible values of b. </p>

40 <p>Testing for 10; </p>

39 <p>Testing for 10; </p>

41 <p>25 = 10×b/10 </p>

40 <p>25 = 10×b/10 </p>

42 <p>b = 25</p>

41 <p>b = 25</p>

43 <p>Testing for 5; </p>

42 <p>Testing for 5; </p>

44 <p>25 = 10×b/5 </p>

43 <p>25 = 10×b/5 </p>

45 <p>b = 12.5 </p>

44 <p>b = 12.5 </p>

46 <p>Testing for 2; </p>

45 <p>Testing for 2; </p>

47 <p>25 = 10×b/2 </p>

46 <p>25 = 10×b/2 </p>

48 <p>b = 5</p>

47 <p>b = 5</p>

49 <p>Testing for 1; </p>

48 <p>Testing for 1; </p>

50 <p>25 =10×b/1 </p>

49 <p>25 =10×b/1 </p>

51 <p>b = 2.5 → cannot be true, 2.5 is not a whole number</p>

50 <p>b = 2.5 → cannot be true, 2.5 is not a whole number</p>

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 <p>b is possibly one of 5 and 25. </p>

52 <p>b is possibly one of 5 and 25. </p>

54 <p>Well explained 👍</p>

53 <p>Well explained 👍</p>

55 <h3>Problem 2</h3>

54 <h3>Problem 2</h3>

56 <p>If a number is 40% of the LCM of 10 and 25, find the number.</p>

55 <p>If a number is 40% of the LCM of 10 and 25, find the number.</p>

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

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

58 <p>LCM of 10,25 = 50</p>

57 <p>LCM of 10,25 = 50</p>

59 <p>40% of 50 → 40/100×50 = 20 </p>

58 <p>40% of 50 → 40/100×50 = 20 </p>

60 <h3>Explanation</h3>

59 <h3>Explanation</h3>

61 <p>40% of the LCM is 20. </p>

60 <p>40% of the LCM is 20. </p>

62 <p>Well explained 👍</p>

61 <p>Well explained 👍</p>

63 <h3>Problem 3</h3>

62 <h3>Problem 3</h3>

64 <p>Trains A and B arrive every 10 minutes and 25 minutes at the station at the same time. In how long will they arrive together again?</p>

63 <p>Trains A and B arrive every 10 minutes and 25 minutes at the station at the same time. In how long will they arrive together again?</p>

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

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

66 <p>The LCM of 10 and 25 = 50 </p>

65 <p>The LCM of 10 and 25 = 50 </p>

67 <h3>Explanation</h3>

66 <h3>Explanation</h3>

68 <p>The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 25 minutes. </p>

67 <p>The smallest common multiple is ascertained between the numbers to ascertain the next arrival of the trains at the same time, which is in 25 minutes. </p>

69 <p>Well explained 👍</p>

68 <p>Well explained 👍</p>

70 <h2>FAQ’s on LCM of 10 and 25</h2>

69 <h2>FAQ’s on LCM of 10 and 25</h2>

71 <h3>1.What is the relationship between the HCF and LCM of 10 and 25?</h3>

70 <h3>1.What is the relationship between the HCF and LCM of 10 and 25?</h3>

72 <p>HCF(a,b)×LCM(a,b)=a×b</p>

71 <p>HCF(a,b)×LCM(a,b)=a×b</p>

73 <p>HCF of 10,25 → 5 </p>

72 <p>HCF of 10,25 → 5 </p>

74 <p>LCM of 10,25 → 50 </p>

73 <p>LCM of 10,25 → 50 </p>

75 <p>5×50=10×25</p>

74 <p>5×50=10×25</p>

76 <p>250 = 250 </p>

75 <p>250 = 250 </p>

77 <h3>2.What is the LCM of 10,25,35 and 40?</h3>

76 <h3>2.What is the LCM of 10,25,35 and 40?</h3>

78 <p>Prime factorization of 10 = 2×5</p>

77 <p>Prime factorization of 10 = 2×5</p>

79 <p>Prime factorization of 25= 5×5</p>

78 <p>Prime factorization of 25= 5×5</p>

80 <p>Prime factorization of 35 = 5×7</p>

79 <p>Prime factorization of 35 = 5×7</p>

81 <p>Prime factorization of 40 = 5×2×2×2</p>

80 <p>Prime factorization of 40 = 5×2×2×2</p>

82 <p>LCM (10,25,35,40) = 1400 </p>

81 <p>LCM (10,25,35,40) = 1400 </p>

83 <h3>3.What is the LCM of 10 and 25?</h3>

82 <h3>3.What is the LCM of 10 and 25?</h3>

84 <p>Prime factorization of 10 = 2×5</p>

83 <p>Prime factorization of 10 = 2×5</p>

85 <p>Prime factorization of 25 = 5×5</p>

84 <p>Prime factorization of 25 = 5×5</p>

86 <p>LCM (10,25) = 50 </p>

85 <p>LCM (10,25) = 50 </p>

87 <h3>4.What is the LCM of 9 and 25?</h3>

86 <h3>4.What is the LCM of 9 and 25?</h3>

88 <p>Prime factorization of 9 = 3×3</p>

87 <p>Prime factorization of 9 = 3×3</p>

89 <p>Prime factorization of 25= 5×5</p>

88 <p>Prime factorization of 25= 5×5</p>

90 <p>LCM(9,25) = 225 </p>

89 <p>LCM(9,25) = 225 </p>

91 <h3>5.What is the LCM of 10 and 24?</h3>

90 <h3>5.What is the LCM of 10 and 24?</h3>

92 <p>Prime factorization of 10 = 2×5</p>

91 <p>Prime factorization of 10 = 2×5</p>

93 <p>Prime factorization of 24 = 2×2×2×3</p>

92 <p>Prime factorization of 24 = 2×2×2×3</p>

94 <p>LCM (10,24) = 60 </p>

93 <p>LCM (10,24) = 60 </p>

95 <h2>Important glossaries for LCM of 10 and 25</h2>

94 <h2>Important glossaries for LCM of 10 and 25</h2>

96 <ul><li><strong>Multiple:</strong>A number and any integer multiplied. </li>

95 <ul><li><strong>Multiple:</strong>A number and any integer multiplied. </li>

97 </ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>

96 </ul><ul><li><strong>Prime Factor:</strong>A natural number (other than 1) that has factors that are one and itself.</li>

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

97 </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>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </li>

98 </ul><ul><li><strong>Co-prime numbers:</strong>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </li>

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

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

101 <p>▶</p>

100 <p>▶</p>

102 <h2>Hiralee Lalitkumar Makwana</h2>

101 <h2>Hiralee Lalitkumar Makwana</h2>

103 <h3>About the Author</h3>

102 <h3>About the Author</h3>

104 <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>

103 <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>

105 <h3>Fun Fact</h3>

104 <h3>Fun Fact</h3>

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

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