LCM of 63 and 21
LCM of 63 and 21 is the smallest number among all common multiples of 63 and 21. The first few multiples of 63 and 21 are (63, 126, 189, 252, . . . ) and (21, 42, 63, 84, 105, 126, . . . ) respectively. There are 3 commonly used methods to find LCM of 63 and 21  by division method, by prime factorization, and by listing multiples.
1.  LCM of 63 and 21 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 63 and 21?
Answer: LCM of 63 and 21 is 63.
Explanation:
The LCM of two nonzero integers, x(63) and y(21), is the smallest positive integer m(63) that is divisible by both x(63) and y(21) without any remainder.
Methods to Find LCM of 63 and 21
Let's look at the different methods for finding the LCM of 63 and 21.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 63 and 21 by Division Method
To calculate the LCM of 63 and 21 by the division method, we will divide the numbers(63, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 63 and 21.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 63 and 21. Write this prime number(3) on the left of the given numbers(63 and 21), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (63, 21) is a multiple of 3, divide it by 3 and write the quotient below it. Bring down any number that is not divisible by the prime number.
 Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 63 and 21 is the product of all prime numbers on the left, i.e. LCM(63, 21) by division method = 3 × 3 × 7 = 63.
LCM of 63 and 21 by Listing Multiples
To calculate the LCM of 63 and 21 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 63 (63, 126, 189, 252, . . . ) and 21 (21, 42, 63, 84, 105, 126, . . . . )
 Step 2: The common multiples from the multiples of 63 and 21 are 63, 126, . . .
 Step 3: The smallest common multiple of 63 and 21 is 63.
∴ The least common multiple of 63 and 21 = 63.
LCM of 63 and 21 by Prime Factorization
Prime factorization of 63 and 21 is (3 × 3 × 7) = 3^{2} × 7^{1} and (3 × 7) = 3^{1} × 7^{1} respectively. LCM of 63 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3^{2} × 7^{1} = 63.
Hence, the LCM of 63 and 21 by prime factorization is 63.
☛ Also Check:
 LCM of 144 and 169  24336
 LCM of 8, 9 and 25  1800
 LCM of 27 and 63  189
 LCM of 18 and 28  252
 LCM of 30 and 60  60
 LCM of 15 and 21  105
 LCM of 15 and 16  240
LCM of 63 and 21 Examples

Example 1: Find the smallest number that is divisible by 63 and 21 exactly.
Solution:
The smallest number that is divisible by 63 and 21 exactly is their LCM.
⇒ Multiples of 63 and 21: Multiples of 63 = 63, 126, 189, 252, 315, 378, 441, . . . .
 Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, . . . .
Therefore, the LCM of 63 and 21 is 63.

Example 2: The GCD and LCM of two numbers are 21 and 63 respectively. If one number is 63, find the other number.
Solution:
Let the other number be m.
∵ GCD × LCM = 63 × m
⇒ m = (GCD × LCM)/63
⇒ m = (21 × 63)/63
⇒ m = 21
Therefore, the other number is 21. 
Example 3: The product of two numbers is 1323. If their GCD is 21, what is their LCM?
Solution:
Given: GCD = 21
product of numbers = 1323
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1323/21
Therefore, the LCM is 63.
The probable combination for the given case is LCM(63, 21) = 63.
FAQs on LCM of 63 and 21
What is the LCM of 63 and 21?
The LCM of 63 and 21 is 63. To find the LCM of 63 and 21, we need to find the multiples of 63 and 21 (multiples of 63 = 63, 126, 189, 252; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 63 and 21, i.e., 63.
What are the Methods to Find LCM of 63 and 21?
The commonly used methods to find the LCM of 63 and 21 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
What is the Relation Between GCF and LCM of 63, 21?
The following equation can be used to express the relation between GCF and LCM of 63 and 21, i.e. GCF × LCM = 63 × 21.
If the LCM of 21 and 63 is 63, Find its GCF.
LCM(21, 63) × GCF(21, 63) = 21 × 63
Since the LCM of 21 and 63 = 63
⇒ 63 × GCF(21, 63) = 1323
Therefore, the greatest common factor = 1323/63 = 21.
How to Find the LCM of 63 and 21 by Prime Factorization?
To find the LCM of 63 and 21 using prime factorization, we will find the prime factors, (63 = 3 × 3 × 7) and (21 = 3 × 7). LCM of 63 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 63 and 21.
⇒ LCM of 63, 21 = 3^{2} × 7^{1} = 63.
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