LCM of 3 and 7

LCM of 3 and 7 is the smallest number among all common multiples of 3 and 7. The first few multiples of 3 and 7 are (3, 6, 9, 12, 15, 18, . . . ) and (7, 14, 21, 28, 35, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 7 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 3 and 7 is 21.

Explanation:

The LCM of two non-zero integers, x(3) and y(7), is the smallest positive integer m(21) that is divisible by both x(3) and y(7) without any remainder.

The methods to find the LCM of 3 and 7 are explained below.

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

LCM of 3 and 7 by Prime Factorization

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

LCM of 3 and 7 by Listing Multiples

To calculate the LCM of 3 and 7 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, . . . ) and 7 (7, 14, 21, 28, 35, . . . . )
• Step 2: The common multiples from the multiples of 3 and 7 are 21, 42, . . .
• Step 3: The smallest common multiple of 3 and 7 is 21.

∴ The least common multiple of 3 and 7 = 21.

LCM of 3 and 7 by Division Method

To calculate the LCM of 3 and 7 by the division method, we will divide the numbers(3, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 7.

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

☛ Also Check:

• LCM of 24 and 26 - 312
• LCM of 3, 4 and 8 - 24
• LCM of 2, 3 and 5 - 30
• LCM of 8, 9 and 12 - 72
• LCM of 24, 15 and 36 - 360
• LCM of 4 and 30 - 60
• LCM of 2, 3 and 6 - 6

FAQs on LCM of 3 and 7

What is the LCM of 3 and 7?

The LCM of 3 and 7 is 21. To find the LCM of 3 and 7, we need to find the multiples of 3 and 7 (multiples of 3 = 3, 6, 9, 12 . . . . 21; multiples of 7 = 7, 14, 21, 28) and choose the smallest multiple that is exactly divisible by 3 and 7, i.e., 21.

If the LCM of 7 and 3 is 21, Find its GCF.

LCM(7, 3) × GCF(7, 3) = 7 × 3
Since the LCM of 7 and 3 = 21
⇒ 21 × GCF(7, 3) = 21
Therefore, the greatest common factor (GCF) = 21/21 = 1.

What are the Methods to Find LCM of 3 and 7?

The commonly used methods to find the LCM of 3 and 7 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

How to Find the LCM of 3 and 7 by Prime Factorization?

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

Which of the following is the LCM of 3 and 7? 21, 32, 12, 20

The value of LCM of 3, 7 is the smallest common multiple of 3 and 7. The number satisfying the given condition is 21.