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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 8 and 14. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.</p>

4 <h2>What is the LCM of 8 and 14?</h2>

5 <h2>How to find the LCM of 8 and 14 ?</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 8 and 14 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 8 = 8,16,24,32,40,48,56,…</p>

11 <p>Multiples of 14 = 14,28,42,56,…</p>

12 <p><strong>Step 2:</strong>Ascertain the smallest multiple from the listed multiples of 8 and 14. </p>

13 <p>The LCM (Least common multiple) of 8 and 14 is 56. i.e., 56 is divisible by 8 and 14 with no reminder. </p>

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16 <h3>LCM of 8 and 14 using the Prime Factorization</h3>

15 <h3>LCM of 8 and 14 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 8 = 2×2×2</p>

18 <p>Prime factorization of 8 = 2×2×2</p>

20 <p>Prime factorization of 14 = 2×7</p>

19 <p>Prime factorization of 14 = 2×7</p>

21 <p><strong> Step 2:</strong>Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

20 <p><strong> Step 2:</strong>Take the highest power of each prime factor and multiply the ascertained factors to get the LCM: </p>

22 <p>LCM (8,14) =<strong>56</strong></p>

21 <p>LCM (8,14) =<strong>56</strong></p>

23 <h3>LCM of 8 and 14 using the Division Method</h3>

22 <h3>LCM of 8 and 14 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 4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

27 <p> <strong>Step 4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

29 <p>LCM (8,14) =<strong>56</strong></p>

28 <p>LCM (8,14) =<strong>56</strong></p>

30 <h2>Common Mistakes and how to avoid them while finding the LCM of 8 and 14</h2>

29 <h2>Common Mistakes and how to avoid them while finding the LCM of 8 and 14</h2>

31 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 14, make a note while practicing. </p>

30 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 8 and 14, make a note while practicing. </p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>LCM (x,14) = 56. Find x.</p>

32 <p>LCM (x,14) = 56. Find x.</p>

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

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

35 <p>LCM (x,14) = x×14/HCF (x,14)</p>

34 <p>LCM (x,14) = x×14/HCF (x,14)</p>

36 <p>56 = x×14/HCF(x,14)</p>

35 <p>56 = x×14/HCF(x,14)</p>

37 <p>x= 56×n/14 = 4n</p>

36 <p>x= 56×n/14 = 4n</p>

38 <p>Divisors of 14-1,2,7,14 so n can be only one of them</p>

37 <p>Divisors of 14-1,2,7,14 so n can be only one of them</p>

39 <p> If n = 1 → 56×1/14 = 4</p>

38 <p> If n = 1 → 56×1/14 = 4</p>

40 <p>If n = 2 → 56×2/14 = 8</p>

39 <p>If n = 2 → 56×2/14 = 8</p>

41 <p>If n = 7 → 56×7/14 = 28</p>

40 <p>If n = 7 → 56×7/14 = 28</p>

42 <p>If n = 14 → 56×14/14 = 56 </p>

41 <p>If n = 14 → 56×14/14 = 56 </p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p> From the above we find that the value of x can be anyone from 4,8,28 or 56. </p>

43 <p> From the above we find that the value of x can be anyone from 4,8,28 or 56. </p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>A common multiple of 8 and 14 is expressed as n. If n is the smallest integer greater than 50, find the value of n.</p>

46 <p>A common multiple of 8 and 14 is expressed as n. If n is the smallest integer greater than 50, find the value of n.</p>

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

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

49 <p>We know that the LCM(8,14) = 56 </p>

48 <p>We know that the LCM(8,14) = 56 </p>

50 <p>To ascertain the smallest multiple of 56 greater than 50, we check the multiples of the number 56, </p>

49 <p>To ascertain the smallest multiple of 56 greater than 50, we check the multiples of the number 56, </p>

51 <p>→ 56,112,168,… </p>

50 <p>→ 56,112,168,… </p>

52 <p>The smallest multiple of 56, greater than 50 is 56.</p>

51 <p>The smallest multiple of 56, greater than 50 is 56.</p>

53 <p>n = 56 </p>

52 <p>n = 56 </p>

54 <h3>Explanation</h3>

53 <h3>Explanation</h3>

55 <p>The above is how we find the smallest integer greater than a given number. </p>

54 <p>The above is how we find the smallest integer greater than a given number. </p>

56 <p>Well explained 👍</p>

55 <p>Well explained 👍</p>

57 <h3>Problem 3</h3>

56 <h3>Problem 3</h3>

58 <p>Trains A and B arrive every 8 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?</p>

57 <p>Trains A and B arrive every 8 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?</p>

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

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

60 <p>The LCM of 8 and 14 =14. </p>

59 <p>The LCM of 8 and 14 =14. </p>

61 <h3>Explanation</h3>

60 <h3>Explanation</h3>

62 <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 14 minutes. </p>

61 <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 14 minutes. </p>

63 <p>Well explained 👍</p>

62 <p>Well explained 👍</p>

64 <h2>FAQ’s on LCM of 8 and 14</h2>

63 <h2>FAQ’s on LCM of 8 and 14</h2>

65 <h3>1. What is the HCF of 8 and 14?</h3>

64 <h3>1. What is the HCF of 8 and 14?</h3>

66 <p>Factors of 8 = 1,2,4,8</p>

65 <p>Factors of 8 = 1,2,4,8</p>

67 <p>Factors of 14 = 1,2,7,14</p>

66 <p>Factors of 14 = 1,2,7,14</p>

68 <p>HCF (8,14) = 2 </p>

67 <p>HCF (8,14) = 2 </p>

69 <h3>2.What is the LCM 8,14 and 16?</h3>

68 <h3>2.What is the LCM 8,14 and 16?</h3>

70 <p>Prime factorization of 8 = 2×2×2</p>

69 <p>Prime factorization of 8 = 2×2×2</p>

71 <p>Prime factorization of 14 = 2×7</p>

70 <p>Prime factorization of 14 = 2×7</p>

72 <p>Prime factorization of 16 = 2×2×2×2</p>

71 <p>Prime factorization of 16 = 2×2×2×2</p>

73 <p>LCM (8,14,16) = 112 </p>

72 <p>LCM (8,14,16) = 112 </p>

74 <h3>3. What is the LCM of 8 and 12?</h3>

73 <h3>3. What is the LCM of 8 and 12?</h3>

75 <p>Prime factorization of 8 = 2×2×2</p>

74 <p>Prime factorization of 8 = 2×2×2</p>

76 <p>Prime factorization of 12 = 2×2×3</p>

75 <p>Prime factorization of 12 = 2×2×3</p>

77 <p>LCM (8,12) =24 </p>

76 <p>LCM (8,12) =24 </p>

78 <h3>4.What is the LCM 8,14 and 12?</h3>

77 <h3>4.What is the LCM 8,14 and 12?</h3>

79 <p>Prime factorization of 8 = 2×2×2</p>

78 <p>Prime factorization of 8 = 2×2×2</p>

80 <p>Prime factorization of 14 = 2×7</p>

79 <p>Prime factorization of 14 = 2×7</p>

81 <p>Prime factorization of 12 = 2×2×3</p>

80 <p>Prime factorization of 12 = 2×2×3</p>

82 <p>LCM (8,14,12) = 168 </p>

81 <p>LCM (8,14,12) = 168 </p>

83 <h3>5.What is the LCM of 9 and 14?</h3>

82 <h3>5.What is the LCM of 9 and 14?</h3>

84 <p>Prime factorization of 14 = 2×7</p>

83 <p>Prime factorization of 14 = 2×7</p>

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

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

86 <p>LCM (9,14) = 126 </p>

85 <p>LCM (9,14) = 126 </p>

87 <h2>Important glossaries for LCM of 8 and 14</h2>

86 <h2>Important glossaries for LCM of 8 and 14</h2>

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

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

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

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

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

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

91 </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>

90 </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>

92 </ul><ul><li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>

91 </ul><ul><li><strong>Relatively Prime Numbers:</strong>Numbers that have no common factors other than 1.</li>

93 </ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole. </li>

92 </ul><ul><li><strong>Fraction:</strong>A representation of a part of a whole. </li>

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

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

95 <p>▶</p>

94 <p>▶</p>

96 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h2>Hiralee Lalitkumar Makwana</h2>

97 <h3>About the Author</h3>

96 <h3>About the Author</h3>

98 <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>

97 <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>

99 <h3>Fun Fact</h3>

98 <h3>Fun Fact</h3>

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

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