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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 21 and 28. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. In our daily life, we use application of LCM for setting alarms in our clock or coordinating any orders.</p>

4 <h2>What is the LCM of 21 and 28?</h2>

5 <h2>How to find the LCM of 21 and 28 ?</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 21 and 28 using the Listing Multiples method</h3>

8 <p>The LCM of 21 and 28 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 21 = 21,42,63,84,105,126,147,168,…</p>

11 <p>Multiples of 28 = 28,56,84,112,140,168,196,…</p>

12 <p><strong>Step 2: </strong>Ascertain the smallest multiple from the listed multiples of 21 and 28. </p>

13 <p>The LCM (The Least<a>common multiple</a>) of 21 and 28 is 84, i.e.,84 is divisible by 21 and 28 leaving no reminders. </p>

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16 <h3>LCM of 21 and 28 using the Prime Factorization</h3>

15 <h3>LCM of 21 and 28 using the Prime Factorization</h3>

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

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

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

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

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

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

20 <p>Prime factorization of 28 = 2×2×7</p>

19 <p>Prime factorization of 28 = 2×2×7</p>

21 <p>Step 2:Take the highest power of each prime factor:</p>

20 <p>Step 2:Take the highest power of each prime factor:</p>

22 <p>Step 3: Multiply the ascertained factors to get the LCM: </p>

21 <p>Step 3: Multiply the ascertained factors to get the LCM: </p>

23 <p>LCM (21,28) = 84</p>

22 <p>LCM (21,28) = 84</p>

24 <h3>LCM of 21 and 28 using the Division method</h3>

23 <h3>LCM of 21 and 28 using the Division method</h3>

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

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

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

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

27 <p>Step 2:Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.</p>

26 <p>Step 2:Divide the row of numbers by a<a>prime number</a>that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.</p>

28 <p> Step 3:The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e, </p>

27 <p> Step 3:The LCM of the numbers is the<a>product</a>of the prime numbers in the first column, i.e, </p>

29 <p>LCM (21,28) = 84</p>

28 <p>LCM (21,28) = 84</p>

30 <h2>Common Mistakes and how to avoid them in LCM of 21 and 28</h2>

29 <h2>Common Mistakes and how to avoid them in LCM of 21 and 28</h2>

31 <p>here some common mistake with their solutions are given:</p>

30 <p>here some common mistake with their solutions are given:</p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>LCM of 21 and b is 84. HCF of the same is 7. Find b.</p>

32 <p>LCM of 21 and b is 84. HCF of the same is 7. Find b.</p>

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

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

35 <p>The following relationship can be used to find the other number b. </p>

34 <p>The following relationship can be used to find the other number b. </p>

36 <p>LCM×HCF=Product of the two numbers </p>

35 <p>LCM×HCF=Product of the two numbers </p>

37 <p>Substituting into the formula: </p>

36 <p>Substituting into the formula: </p>

38 <p>84×7 = 21×b</p>

37 <p>84×7 = 21×b</p>

39 <p>588 = 21b</p>

38 <p>588 = 21b</p>

40 <p>b= 28 </p>

39 <p>b= 28 </p>

41 <h3>Explanation</h3>

40 <h3>Explanation</h3>

42 <p>The above is how we find the other number when the LCM, HCF, and one of the numbers is given.</p>

41 <p>The above is how we find the other number when the LCM, HCF, and one of the numbers is given.</p>

43 <p>Well explained 👍</p>

42 <p>Well explained 👍</p>

44 <h3>Problem 2</h3>

43 <h3>Problem 2</h3>

45 <p>Find x such that both 21 and 28 are its factors.</p>

44 <p>Find x such that both 21 and 28 are its factors.</p>

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

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

47 <p>The LCM of 21 and 28 = 84 </p>

46 <p>The LCM of 21 and 28 = 84 </p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>the smallest number both 21 and 28 divide is the LCM of the numbers itself. All multiples of 84 are factored by 21 and 28. </p>

48 <p>the smallest number both 21 and 28 divide is the LCM of the numbers itself. All multiples of 84 are factored by 21 and 28. </p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>Solve for the LCM of 21 and 28 using → LCM(a,b)=a×b/HCF(a,b)</p>

51 <p>Solve for the LCM of 21 and 28 using → LCM(a,b)=a×b/HCF(a,b)</p>

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

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

54 <p>HCF of 21 and 28 → 7 </p>

53 <p>HCF of 21 and 28 → 7 </p>

55 <p>Applying the values in the formula;</p>

54 <p>Applying the values in the formula;</p>

56 <p> LCM(a,b)=a×b/HCF(a,b)</p>

55 <p> LCM(a,b)=a×b/HCF(a,b)</p>

57 <p>LCM(21,28)=21×28/7</p>

56 <p>LCM(21,28)=21×28/7</p>

58 <p>LCM(21,28) = 84 </p>

57 <p>LCM(21,28) = 84 </p>

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 <p>By applying the formula as above, we can ascertain the LCM of two numbers directly without using the prime factorization or other methods. </p>

59 <p>By applying the formula as above, we can ascertain the LCM of two numbers directly without using the prime factorization or other methods. </p>

61 <p>Well explained 👍</p>

60 <p>Well explained 👍</p>

62 <h2>FAQs on LCM of 21 and 28</h2>

61 <h2>FAQs on LCM of 21 and 28</h2>

63 <h3>1.What is the LCM of 12 and 28?</h3>

62 <h3>1.What is the LCM of 12 and 28?</h3>

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

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

65 <p>Prime factorization of 28 = 2×2×7</p>

64 <p>Prime factorization of 28 = 2×2×7</p>

66 <p>LCM(12,28) = 84 </p>

65 <p>LCM(12,28) = 84 </p>

67 <h3>2.What is the LCM of 21,24 and 28?</h3>

66 <h3>2.What is the LCM of 21,24 and 28?</h3>

68 <p>Prime factorization of 28 = 2×2×7</p>

67 <p>Prime factorization of 28 = 2×2×7</p>

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

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

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

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

71 <p>LCM (21,24,28) = 168 </p>

70 <p>LCM (21,24,28) = 168 </p>

72 <h3>3.What is the LCM of 21 and 27?</h3>

71 <h3>3.What is the LCM of 21 and 27?</h3>

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

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

74 <p>Prime factorization of 27 = 3×3×3</p>

73 <p>Prime factorization of 27 = 3×3×3</p>

75 <p>LCM (21,27) = 189 </p>

74 <p>LCM (21,27) = 189 </p>

76 <h3>4.What is the LCM of 14,21 and 28?</h3>

75 <h3>4.What is the LCM of 14,21 and 28?</h3>

77 <p>Prime factorization of 28 = 2×2×7</p>

76 <p>Prime factorization of 28 = 2×2×7</p>

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

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

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

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

80 <p>LCM (14,21,28) = 84 </p>

79 <p>LCM (14,21,28) = 84 </p>

81 <h3>5.What is the LCM of 21 and 25?</h3>

80 <h3>5.What is the LCM of 21 and 25?</h3>

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

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

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

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

84 <p>LCM(21,25) = 525 </p>

83 <p>LCM(21,25) = 525 </p>

85 <h2>Important glossaries for LCM of 21 and 28</h2>

84 <h2>Important glossaries for LCM of 21 and 28</h2>

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

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

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

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

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

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

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

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

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

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

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

93 <p>▶</p>

92 <p>▶</p>

94 <h2>Hiralee Lalitkumar Makwana</h2>

93 <h2>Hiralee Lalitkumar Makwana</h2>

95 <h3>About the Author</h3>

94 <h3>About the Author</h3>

96 <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>

95 <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 <h3>Fun Fact</h3>

96 <h3>Fun Fact</h3>

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

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