LCM of 21 and 97

LCM of 21 and 97 is the smallest number among all common multiples of 21 and 97. The first few multiples of 21 and 97 are (21, 42, 63, 84, . . . ) and (97, 194, 291, 388, 485, . . . ) respectively. There are 3 commonly used methods to find LCM of 21 and 97 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 21 and 97 is 2037.

Explanation:

The LCM of two non-zero integers, x(21) and y(97), is the smallest positive integer m(2037) that is divisible by both x(21) and y(97) without any remainder.

Let's look at the different methods for finding the LCM of 21 and 97.

• By Listing Multiples
• By Prime Factorization Method
• By Division Method

LCM of 21 and 97 by Listing Multiples

To calculate the LCM of 21 and 97 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 21 (21, 42, 63, 84, . . . ) and 97 (97, 194, 291, 388, 485, . . . . )
• Step 2: The common multiples from the multiples of 21 and 97 are 2037, 4074, . . .
• Step 3: The smallest common multiple of 21 and 97 is 2037.

∴ The least common multiple of 21 and 97 = 2037.

LCM of 21 and 97 by Prime Factorization

Prime factorization of 21 and 97 is (3 × 7) = 3¹ × 7¹ and (97) = 97¹ respectively. LCM of 21 and 97 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 7¹ × 97¹ = 2037.
Hence, the LCM of 21 and 97 by prime factorization is 2037.

LCM of 21 and 97 by Division Method

To calculate the LCM of 21 and 97 by the division method, we will divide the numbers(21, 97) by their prime factors (preferably common). The product of these divisors gives the LCM of 21 and 97.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 21 and 97. Write this prime number(3) on the left of the given numbers(21 and 97), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (21, 97) 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 21 and 97 is the product of all prime numbers on the left, i.e. LCM(21, 97) by division method = 3 × 7 × 97 = 2037.

☛ Also Check:

• LCM of 12 and 22 - 132
• LCM of 12 and 28 - 84
• LCM of 24 and 8 - 24
• LCM of 42 and 48 - 336
• LCM of 18 and 36 - 36
• LCM of 13 and 11 - 143
• LCM of 56 and 98 - 392

FAQs on LCM of 21 and 97

What is the LCM of 21 and 97?

The LCM of 21 and 97 is 2037. To find the least common multiple (LCM) of 21 and 97, we need to find the multiples of 21 and 97 (multiples of 21 = 21, 42, 63, 84 . . . . 2037; multiples of 97 = 97, 194, 291, 388 . . . . 2037) and choose the smallest multiple that is exactly divisible by 21 and 97, i.e., 2037.

What is the Relation Between GCF and LCM of 21, 97?

The following equation can be used to express the relation between GCF and LCM of 21 and 97, i.e. GCF × LCM = 21 × 97.

What are the Methods to Find LCM of 21 and 97?

The commonly used methods to find the LCM of 21 and 97 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

If the LCM of 97 and 21 is 2037, Find its GCF.

LCM(97, 21) × GCF(97, 21) = 97 × 21
Since the LCM of 97 and 21 = 2037
⇒ 2037 × GCF(97, 21) = 2037
Therefore, the greatest common factor = 2037/2037 = 1.

How to Find the LCM of 21 and 97 by Prime Factorization?

To find the LCM of 21 and 97 using prime factorization, we will find the prime factors, (21 = 3 × 7) and (97 = 97). LCM of 21 and 97 is the product of prime factors raised to their respective highest exponent among the numbers 21 and 97.
⇒ LCM of 21, 97 = 3¹ × 7¹ × 97¹ = 2037.