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3 The Least common multiple (LCM) is the smallest number that is divisible by the numbers 14 and 21. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

4 <h2>What is the LCM of 14 and 21?</h2>

5 <h2>How to find the LCM of 14 and 21?</h2>

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

7 <h3>LCM of 14 and 21 using the Listing multiples method</h3>

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

9 Steps:

10 1. Write down the multiples of each number:

11 Multiples of 14 = 14,28,42,…

12 Multiples of 21= 21,42,63…

13 2. Ascertain the smallest multiple from the listed multiples

14 The<a>least common multiple</a>of the numbers is 42.

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17 <h3>LCM of 14 and 21 using the Prime Factorization</h3>

16 <h3>LCM of 14 and 21 using the Prime Factorization</h3>

18 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.

17 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.

19 Steps:

18 Steps:

20 1. Find the prime factors of the numbers:

19 1. Find the prime factors of the numbers:

21 Prime factorization of 14 = 2×7

20 Prime factorization of 14 = 2×7

22 Prime factorization of 21= 3×7

21 Prime factorization of 21= 3×7

23 2. Take the highest power of each prime factor and multiply the ascertained factors.

22 2. Take the highest power of each prime factor and multiply the ascertained factors.

24 - LCM = 42

23 - LCM = 42

25 <h3>LCM of 14 and 21 using the Division Method</h3>

24 <h3>LCM of 14 and 21 using the Division Method</h3>

26 The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.

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

27 Steps:

26 Steps:

28 1. Write down the numbers in a row;

27 1. Write down the numbers in a row;

29 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 not divisible by the previously chosen prime number.

28 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 not divisible by the previously chosen prime number.

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

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

31 2×7×3 = 42

30 2×7×3 = 42

32 <h2>Common Mistakes and how to avoid them while finding the LCM of 14 and 21</h2>

31 <h2>Common Mistakes and how to avoid them while finding the LCM of 14 and 21</h2>

33 Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 14 and 21, make a note while practicing.

32 Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 14 and 21, make a note while practicing.

34 <h3>Problem 1</h3>

33 <h3>Problem 1</h3>

35 Ram goes to the office canteen every 14 days, and his boss goes every 21 days. After how many days will they meet on the same day again?

34 Ram goes to the office canteen every 14 days, and his boss goes every 21 days. After how many days will they meet on the same day again?

36 Okay, lets begin

35 Okay, lets begin

37 The LCM of 14 and 21 is 42.

36 The LCM of 14 and 21 is 42.

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 They will meet again on the same day in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

38 They will meet again on the same day in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

40 Well explained 👍

39 Well explained 👍

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 Machine X stops for maintenance every 14 hours, while machine Y stops every 21 hours. In how long will the machines stop again?

41 Machine X stops for maintenance every 14 hours, while machine Y stops every 21 hours. In how long will the machines stop again?

43 Okay, lets begin

42 Okay, lets begin

44 The LCM of 14 and 21 is 42.

43 The LCM of 14 and 21 is 42.

45 <h3>Explanation</h3>

44 <h3>Explanation</h3>

46 The machines will stop every 42 hours. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

45 The machines will stop every 42 hours. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

47 Well explained 👍

46 Well explained 👍

48 <h3>Problem 3</h3>

47 <h3>Problem 3</h3>

49 A store receives shipments of apples every 14 days and pineapples every 21 days. If both shipments arrive today, in how many days will both shipments arrive again on the same day?

48 A store receives shipments of apples every 14 days and pineapples every 21 days. If both shipments arrive today, in how many days will both shipments arrive again on the same day?

50 Okay, lets begin

49 Okay, lets begin

51 The LCM of 14 and 21 is 42.

50 The LCM of 14 and 21 is 42.

52 <h3>Explanation</h3>

51 <h3>Explanation</h3>

53 Both the shipments will arrive together again in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

52 Both the shipments will arrive together again in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

54 Well explained 👍

53 Well explained 👍

55 <h3>Problem 4</h3>

54 <h3>Problem 4</h3>

56 Leo, and Will, have classroom clean-up duties. Emma is assigned to cleaning duties every 14 days and Jack every 21 days. If both are assigned clean-up today, when will they next be assigned on the same day?

55 Leo, and Will, have classroom clean-up duties. Emma is assigned to cleaning duties every 14 days and Jack every 21 days. If both are assigned clean-up today, when will they next be assigned on the same day?

57 Okay, lets begin

56 Okay, lets begin

58 The LCM of 14 and 21 is 42.

57 The LCM of 14 and 21 is 42.

59 <h3>Explanation</h3>

58 <h3>Explanation</h3>

60 Both of them will be assigned to clean up in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

59 Both of them will be assigned to clean up in 42 days. The LCM of 14 and 21 is 42, which expresses the smallest common time interval between the digits.

61 Well explained 👍

60 Well explained 👍

62 <h2>FAQ’s on LCM of 14 and 21</h2>

61 <h2>FAQ’s on LCM of 14 and 21</h2>

63 <h3>1.What is the relationship between the Greatest Common Divisor (GCD) and LCM of 14 and 21?</h3>

62 <h3>1.What is the relationship between the Greatest Common Divisor (GCD) and LCM of 14 and 21?</h3>

64 The relationship between GCD and LCM is expressed by the<a>formula</a>:

63 The relationship between GCD and LCM is expressed by the<a>formula</a>:

65 LCM(a, b)×HCF(a, b)=a×b

64 LCM(a, b)×HCF(a, b)=a×b

66 Verifying this,

65 Verifying this,

67 LCM (14,21)×HCF (14,21)

66 LCM (14,21)×HCF (14,21)

68 42×7=14×21 -> 294=294

67 42×7=14×21 -> 294=294

69 This formula shows how the GCD and LCM complement each other.

68 This formula shows how the GCD and LCM complement each other.

70 <h3>2.What is the LCM of algebraic expressions?</h3>

69 <h3>2.What is the LCM of algebraic expressions?</h3>

71 For<a>algebraic expressions</a>, find the LCM by factoring each expression and then choosing the highest power of each<a>variable</a>.

70 For<a>algebraic expressions</a>, find the LCM by factoring each expression and then choosing the highest power of each<a>variable</a>.

72 For example ; Find the LCM ofx2yandxy3

71 For example ; Find the LCM ofx2yandxy3

73 Factor each<a>term</a>as follows

72 Factor each<a>term</a>as follows

74 x2y =x2 ×y----> the highest power = x2

73 x2y =x2 ×y----> the highest power = x2

75 xy3 = x × y3 ----> the highest power = y3

74 xy3 = x × y3 ----> the highest power = y3

76 Multiply the highest powers ---->x2y3

75 Multiply the highest powers ---->x2y3

77 LCM(x2y,xy3) = x2y3

76 LCM(x2y,xy3) = x2y3

78 <h3>3.How do you find the LCM with different bases in an exponential equation?</h3>

77 <h3>3.How do you find the LCM with different bases in an exponential equation?</h3>

79 You can find the LCM For<a>exponential equations</a>with different bases by following the below example,

78 You can find the LCM For<a>exponential equations</a>with different bases by following the below example,

80 <ul><li>Find the LCM of 144×212 and 213×143</li>

79 <ul><li>Find the LCM of 144×212 and 213×143</li>

81 <li>Factorize the terms and find the highest power </li>

80 <li>Factorize the terms and find the highest power </li>

82 </ul>Highest power of 14 = 144

81 </ul>Highest power of 14 = 144

83 Highest power of 21= 213

82 Highest power of 21= 213

84 LCM = 144×213

83 LCM = 144×213

85 <h3>4.What is the LCM formula using the HCF ?</h3>

84 <h3>4.What is the LCM formula using the HCF ?</h3>

86 <ul><li>The LCM can be found using the formula: </li>

85 <ul><li>The LCM can be found using the formula: </li>

87 </ul>LCM (a, b)= a×b/HCF(a, b)

86 </ul>LCM (a, b)= a×b/HCF(a, b)

88 For 14 and 21, HCF(14,21)= 7

87 For 14 and 21, HCF(14,21)= 7

89 So, LCM(14,21)=14×21/7 = 42

88 So, LCM(14,21)=14×21/7 = 42

90 <h3>5.How do you derive the LCM of two decimal numbers? Explain using 14.0 and 21.0.</h3>

89 <h3>5.How do you derive the LCM of two decimal numbers? Explain using 14.0 and 21.0.</h3>

91 To derive the LCM of two<a>decimal numbers</a>, follow the below steps;

90 To derive the LCM of two<a>decimal numbers</a>, follow the below steps;

92 First, convert the given decimals to<a>whole numbers</a>. In the given case, 14.0 and 21.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (14,21)= 42

91 First, convert the given decimals to<a>whole numbers</a>. In the given case, 14.0 and 21.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (14,21)= 42

93 <h2>Important glossaries on the LCM of 14 and 21</h2>

92 <h2>Important glossaries on the LCM of 14 and 21</h2>

94 <ul><li>Multiple:A product of a number and any integer.</li>

93 <ul><li>Multiple:A product of a number and any integer.</li>

95 <li>Prime Factor:A prime factor is a natural number, other than 1, whose only factors are 1 and itself.</li>

94 <li>Prime Factor:A prime factor is a natural number, other than 1, whose only factors are 1 and itself.</li>

96 <li>Prime Factorization:The process of breaking down a number into its prime factors.</li>

95 <li>Prime Factorization:The process of breaking down a number into its prime factors.</li>

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

96 <li>Co-prime numbers:A number is co-prime when the only positive integer that is a divisor of them both is 1.</li>

98 <li>Greatest Common Divisor (GCD):The largest positive integer that divides each of two or more integers without leaving a remainder.</li>

97 <li>Greatest Common Divisor (GCD):The largest positive integer that divides each of two or more integers without leaving a remainder.</li>

99 <li>Relatively Prime Numbers:Two numbers that have no common factors other than 1.</li>

98 <li>Relatively Prime Numbers:Two numbers that have no common factors other than 1.</li>

100 <li>Fraction:A number representing a part of a whole.</li>

99 <li>Fraction:A number representing a part of a whole.</li>

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

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

102 ▶

101 ▶

103 <h2>Hiralee Lalitkumar Makwana</h2>

102 <h2>Hiralee Lalitkumar Makwana</h2>

104 <h3>About the Author</h3>

103 <h3>About the Author</h3>

105 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.

104 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.

106 <h3>Fun Fact</h3>

105 <h3>Fun Fact</h3>

107 : She loves to read number jokes and games.

106 : She loves to read number jokes and games.