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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 7 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 7 and 14?</h2>

5 <h2>How to find the LCM of 7 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 7 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>Step1:</strong>Writedown the multiples of each number: </p>

10 <p>Multiples of 7 = 7,14,…</p>

11 <p>Multiples of 14 = 14,28,… </p>

12 <p><strong>Step2:</strong>Ascertain the smallest multiple from the listed multiples of 7 and 14. </p>

13 <p>The LCM (Least common multiple) of 7 and 14 is 14.<a>i</a>.e., 14 is divisible by 7 and 14 with no reminder. </p>

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16 <h3>LCM of 7 and 14 using the Prime Factorization</h3>

15 <h3>LCM of 7 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>Step1: </strong>Find the prime factors of the numbers:</p>

17 <p><strong>Step1: </strong>Find the prime factors of the numbers:</p>

19 <p>Prime factorization of 7 = 7</p>

18 <p>Prime factorization of 7 = 7</p>

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

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

21 <p><strong>Step2:</strong>Take the highest power of each prime factor: 7,2</p>

20 <p><strong>Step2:</strong>Take the highest power of each prime factor: 7,2</p>

22 <p><strong>Step3:</strong>Multiply the ascertained factors to get the LCM: </p>

21 <p><strong>Step3:</strong>Multiply the ascertained factors to get the LCM: </p>

23 <p>LCM (7,14) = 7×2 = 14 </p>

22 <p>LCM (7,14) = 7×2 = 14 </p>

24 <h3>LCM of 7 and 14 using the Division Method</h3>

23 <h3>LCM of 7 and 14 using the Division Method</h3>

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

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

26 <p><strong>Step1: </strong>Write down the numbers in a row;</p>

25 <p><strong>Step1: </strong>Write down the numbers in a row;</p>

27 <p><strong>Step2: </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>

26 <p><strong>Step2: </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>

28 <p><strong>Step3:</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>

27 <p><strong>Step3:</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>

29 <p><strong>Step4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

28 <p><strong>Step4:</strong>The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e., </p>

30 <p>7×2= 14 </p>

29 <p>7×2= 14 </p>

31 <p>LCM (7,14) = 14</p>

30 <p>LCM (7,14) = 14</p>

32 <h2>Common Mistakes and how to avoid them while finding the LCM of 7 and 14</h2>

31 <h2>Common Mistakes and how to avoid them while finding the LCM of 7 and 14</h2>

33 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 14, make a note while practising.</p>

32 <p>Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 7 and 14, make a note while practising.</p>

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 <p>The LCM of 7 and x is 14. Find x.</p>

34 <p>The LCM of 7 and x is 14. Find x.</p>

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

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

37 <p>LCM (7,x) = 14 </p>

36 <p>LCM (7,x) = 14 </p>

38 <p>x = 14 </p>

37 <p>x = 14 </p>

39 <h3>Explanation</h3>

38 <h3>Explanation</h3>

40 <p> The LCM of 7 and x must be 14. In a case where x is smaller, the LCM would not be 14,therefore x = 14. </p>

39 <p> The LCM of 7 and x must be 14. In a case where x is smaller, the LCM would not be 14,therefore x = 14. </p>

41 <p>Well explained 👍</p>

40 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

41 <h3>Problem 2</h3>

43 <p>Verify the relationship between the HCF and the LCM of 7 and 14 using LCM(a,b) × HCF(a,b) = a×b</p>

42 <p>Verify the relationship between the HCF and the LCM of 7 and 14 using LCM(a,b) × HCF(a,b) = a×b</p>

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

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

45 <p>The LCM of 7 and 14;</p>

44 <p>The LCM of 7 and 14;</p>

46 <p>Prime factorization of 7 = 7</p>

45 <p>Prime factorization of 7 = 7</p>

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

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

48 <p>LCM(7,14) = 14 </p>

47 <p>LCM(7,14) = 14 </p>

49 <p>HCF of 7 and 14; </p>

48 <p>HCF of 7 and 14; </p>

50 <p>Factors of 7 = 1,7</p>

49 <p>Factors of 7 = 1,7</p>

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

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

52 <p>HCF(7,14) = 7</p>

51 <p>HCF(7,14) = 7</p>

53 <p>Verify the ascertained LCM and HCF by applying them in the formula;</p>

52 <p>Verify the ascertained LCM and HCF by applying them in the formula;</p>

54 <p>LCM(a,b)×HCF(a,b) =a×b </p>

53 <p>LCM(a,b)×HCF(a,b) =a×b </p>

55 <p>LCM(7,14)×HCF(7,14) =7×14 </p>

54 <p>LCM(7,14)×HCF(7,14) =7×14 </p>

56 <p>14×7 =98 </p>

55 <p>14×7 =98 </p>

57 <p>98 =98 </p>

56 <p>98 =98 </p>

58 <h3>Explanation</h3>

57 <h3>Explanation</h3>

59 <p>Both sides are equal, hence, the relationship between the HCF and LCM of 7 and 14 is verified. </p>

58 <p>Both sides are equal, hence, the relationship between the HCF and LCM of 7 and 14 is verified. </p>

60 <p>Well explained 👍</p>

59 <p>Well explained 👍</p>

61 <h3>Problem 3</h3>

60 <h3>Problem 3</h3>

62 <p>Solve 5/7 + 3/14.</p>

61 <p>Solve 5/7 + 3/14.</p>

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

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

64 <p>To add 5/7 and 3/14, first, find the LCM of their denominators; </p>

63 <p>To add 5/7 and 3/14, first, find the LCM of their denominators; </p>

65 <p>LCM (7,14) = 14 </p>

64 <p>LCM (7,14) = 14 </p>

66 <p>Now, we equate the denominators; </p>

65 <p>Now, we equate the denominators; </p>

67 <p>5/7 × 2/2 = 10/14 </p>

66 <p>5/7 × 2/2 = 10/14 </p>

68 <p>3/14 stays as it is, the denominator is already 14. </p>

67 <p>3/14 stays as it is, the denominator is already 14. </p>

69 <p>Add the fractions; </p>

68 <p>Add the fractions; </p>

70 <p>10/14+3/14 = 13/14 </p>

69 <p>10/14+3/14 = 13/14 </p>

71 <p>The sum is<strong>13/14.</strong> </p>

70 <p>The sum is<strong>13/14.</strong> </p>

72 <h3>Explanation</h3>

71 <h3>Explanation</h3>

73 <p> By equating the denominators of fractions, we can easily perform arithmetic operations on them. </p>

72 <p> By equating the denominators of fractions, we can easily perform arithmetic operations on them. </p>

74 <p>Well explained 👍</p>

73 <p>Well explained 👍</p>

75 <h3>Problem 4</h3>

74 <h3>Problem 4</h3>

76 <p>Trains A and B arrive every 7 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?</p>

75 <p>Trains A and B arrive every 7 minutes and 14 minutes at the station at the same time. In how long will they arrive together again?</p>

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

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

78 <p> The LCM of 7 and 14 =14. </p>

77 <p> The LCM of 7 and 14 =14. </p>

79 <h3>Explanation</h3>

78 <h3>Explanation</h3>

80 <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>

79 <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>

81 <p>Well explained 👍</p>

80 <p>Well explained 👍</p>

82 <h2>FAQ’s on LCM of 7 and 14</h2>

81 <h2>FAQ’s on LCM of 7 and 14</h2>

83 <h3>1.What is the LCM of 7,14 and 21?</h3>

82 <h3>1.What is the LCM of 7,14 and 21?</h3>

84 <p>Prime factorization of 7 = 7</p>

83 <p>Prime factorization of 7 = 7</p>

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

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

86 <p>Prime factorization of 21 = 3×7 </p>

85 <p>Prime factorization of 21 = 3×7 </p>

87 <p>LCM (7,14 and 21) = 2×7×3 = 42 </p>

86 <p>LCM (7,14 and 21) = 2×7×3 = 42 </p>

88 <h3>2.What do 7 and 14 have in common ?</h3>

87 <h3>2.What do 7 and 14 have in common ?</h3>

89 <p>The numbers 7 and 14 share the common factor 7.</p>

88 <p>The numbers 7 and 14 share the common factor 7.</p>

90 <h3>3.List the multiples of 7 and 14.</h3>

89 <h3>3.List the multiples of 7 and 14.</h3>

91 <p>Multiples of 7-7,14,21,28,35,42,49,56,63,70,…</p>

90 <p>Multiples of 7-7,14,21,28,35,42,49,56,63,70,…</p>

92 <p>Multiples of 14-14,28,42,56,70,84,98,112,126,140,… </p>

91 <p>Multiples of 14-14,28,42,56,70,84,98,112,126,140,… </p>

93 <h3>4.Is 7 a factor of 56?</h3>

92 <h3>4.Is 7 a factor of 56?</h3>

94 <p>Yes, 7 is a factor of 56. To verify the same, we divide the numbers. 56/7 = 8. As there is no<a>remainder</a>left behind, we can say that the number 7 is indeed a factor of 56. </p>

93 <p>Yes, 7 is a factor of 56. To verify the same, we divide the numbers. 56/7 = 8. As there is no<a>remainder</a>left behind, we can say that the number 7 is indeed a factor of 56. </p>

95 <h3>5.Is 7 a factor of 360?</h3>

94 <h3>5.Is 7 a factor of 360?</h3>

96 <p>No, 7 is not a factor of 360. To verify the same, we divide the numbers. 360/7= 51.43. As there is a remainder left behind, we can say that the number 7 is not a factor of 360. </p>

95 <p>No, 7 is not a factor of 360. To verify the same, we divide the numbers. 360/7= 51.43. As there is a remainder left behind, we can say that the number 7 is not a factor of 360. </p>

97 <h2>Important glossaries for LCM of 7 and 14</h2>

96 <h2>Important glossaries for LCM of 7 and 14</h2>

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

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

99 </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 Factor:</strong>A natural number (other than 1) that has factors that are one 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>When the only positive integer that is a divisor of them both is 1, a number is co-prime. </li>

100 </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>

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

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

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

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