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LCM of 9 and 21

LCM of 9 and 21 is 63. Students can learn the concept of the least common multiple of 9 and 21 using common multiples from the study materials at BYJU’S. (9, 18, 27, 36, 45, 54, ….) and (21, 42, 63, 84, 105,….) are the multiples of 9 and 21. The LCM of two numbers can be found using the prime factorisation method, by listing the multiples and division methods.

Also read: Least common multiple

What is LCM of 9 and 21?

The answer to this question is 63. The LCM of 9 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 21, is the smallest positive integer 63 which is divisible by both 9 and 21 with no remainder.

lcm of 9 and 21

How to Find LCM of 9 and 21?

LCM of 9 and 21 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 9 and 21 Using Prime Factorisation Method

The prime factorisation of 9 and 21, respectively, is given by:

9 = 3 x 3 = 3² 

21 = 3 x 7 = 3¹ x 7¹

LCM (9, 21) = 63

LCM of 9 and 21 Using Division Method

We’ll divide the numbers (9, 21) by their prime factors to get the LCM of 9 and 21 using the division method (preferably common). The LCM of 9 and 21 is calculated by multiplying these divisors.

3 9 21
3 3 7
7 1 7
x 1 1

No further division can be done. 

Hence, LCM (9, 21) = 63

LCM of 9 and 21 Using Listing the Multiples

To calculate the LCM of 9 and 21 by listing out the common multiples, list the multiples as shown below

Multiples of 9 Multiples of 21
9 21
18 42
27 63
36 84
45 105
54 126
63 147
72 168

The smallest common multiple of 9 and 21 is 63.

Therefore LCM (9, 21) = 63

Related Articles

Video Lesson on Applications of LCM

LCM of 9 and 21 Solved Examples 

What is the LCM if the product of two numbers is 189 and the GCD is 3?

Solution:

It is given that

Product of two numbers = 189

GCD = 3

We know that

LCM x GCD = Product of two numbers

LCM = Product/GCD

LCM = 189/3

LCM = 63

Hence, the LCM is 63.

Frequently Asked Questions on LCM of 9 and 21

What is the LCM of 9 and 21?

The LCM of 9 and 21 is 63. To get the LCM value, we should first find the multiples of 9 and 21 and the value which is divisible by 9 and 21 has to be determined.

What methods can be used to find the LCM value of 9 and 21?

The methods which can be used to find the LCM of 9 and 21 are Division Method, Prime Factorization Method and Listing multiples.

Determine the GCF if the LCM of 9 and 21 is 63.

LCM x GCF = 9 x 21

Given

LCM of 9 and 21 = 63

63 x GCF = 189

GCF = 189/63 = 3

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