LCM of 7 and 21

LCM of 7 and 21 is the smallest number among all common multiples of 7 and 21. The first few multiples of 7 and 21 are (7, 14, 21, 28, 35, 42, 49, . . . ) and (21, 42, 63, 84, 105, 126, 147, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 21 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 7 and 21 is 21.

Explanation:

The LCM of two non-zero integers, x(7) and y(21), is the smallest positive integer m(21) that is divisible by both x(7) and y(21) without any remainder.

The methods to find the LCM of 7 and 21 are explained below.

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

LCM of 7 and 21 by Prime Factorization

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

LCM of 7 and 21 by Division Method

To calculate the LCM of 7 and 21 by the division method, we will divide the numbers(7, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 21.

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

LCM of 7 and 21 by Listing Multiples

To calculate the LCM of 7 and 21 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, 49, . . . ) and 21 (21, 42, 63, 84, 105, 126, 147, . . . . )
• Step 2: The common multiples from the multiples of 7 and 21 are 21, 42, . . .
• Step 3: The smallest common multiple of 7 and 21 is 21.

∴ The least common multiple of 7 and 21 = 21.

☛ Also Check:

• LCM of 48 and 64 - 192
• LCM of 14 and 18 - 126
• LCM of 17 and 5 - 85
• LCM of 36 and 60 - 180
• LCM of 3, 7 and 10 - 210
• LCM of 12, 16 and 18 - 144
• LCM of 5 and 20 - 20

FAQs on LCM of 7 and 21

What is the LCM of 7 and 21?

The LCM of 7 and 21 is 21. To find the LCM of 7 and 21, we need to find the multiples of 7 and 21 (multiples of 7 = 7, 14, 21, 28; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 7 and 21, i.e., 21.

Which of the following is the LCM of 7 and 21? 21, 30, 12, 25

The value of LCM of 7, 21 is the smallest common multiple of 7 and 21. The number satisfying the given condition is 21.

What is the Relation Between GCF and LCM of 7, 21?

The following equation can be used to express the relation between GCF and LCM of 7 and 21, i.e. GCF × LCM = 7 × 21.

How to Find the LCM of 7 and 21 by Prime Factorization?

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

If the LCM of 21 and 7 is 21, Find its GCF.

LCM(21, 7) × GCF(21, 7) = 21 × 7
Since the LCM of 21 and 7 = 21
⇒ 21 × GCF(21, 7) = 147
Therefore, the GCF (greatest common factor) = 147/21 = 7.