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.

Answer: LCM of 63 and 21 is 63.

Explanation:

The LCM of two non-zero 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.

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) = 3² × 7¹ and (3 × 7) = 3¹ × 7¹ respectively. LCM of 63 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 7¹ = 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

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 = 3² × 7¹ = 63.