LCM of 6 and 7

LCM of 6 and 7 is the smallest number among all common multiples of 6 and 7. The first few multiples of 6 and 7 are (6, 12, 18, 24, 30, 36, . . . ) and (7, 14, 21, 28, 35, 42, 49, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 7 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 6 and 7 is 42.

Explanation:

The LCM of two non-zero integers, x(6) and y(7), is the smallest positive integer m(42) that is divisible by both x(6) and y(7) without any remainder.

The methods to find the LCM of 6 and 7 are explained below.

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

LCM of 6 and 7 by Division Method

To calculate the LCM of 6 and 7 by the division method, we will divide the numbers(6, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 7.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 7. Write this prime number(2) on the left of the given numbers(6 and 7), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 7) is a multiple of 2, divide it by 2 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 6 and 7 is the product of all prime numbers on the left, i.e. LCM(6, 7) by division method = 2 × 3 × 7 = 42.

LCM of 6 and 7 by Listing Multiples

To calculate the LCM of 6 and 7 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 7 (7, 14, 21, 28, 35, 42, 49, . . . . )
• Step 2: The common multiples from the multiples of 6 and 7 are 42, 84, . . .
• Step 3: The smallest common multiple of 6 and 7 is 42.

∴ The least common multiple of 6 and 7 = 42.

LCM of 6 and 7 by Prime Factorization

Prime factorization of 6 and 7 is (2 × 3) = 2¹ × 3¹ and (7) = 7¹ respectively. LCM of 6 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 7¹ = 42.
Hence, the LCM of 6 and 7 by prime factorization is 42.

☛ Also Check:

• LCM of 4 and 5 - 20
• LCM of 8, 16 and 24 - 48
• LCM of 5, 8 and 12 - 120
• LCM of 24, 30 and 40 - 120
• LCM of 10 and 11 - 110
• LCM of 36 and 48 - 144
• LCM of 60 and 90 - 180

FAQs on LCM of 6 and 7

What is the LCM of 6 and 7?

The LCM of 6 and 7 is 42. To find the least common multiple of 6 and 7, we need to find the multiples of 6 and 7 (multiples of 6 = 6, 12, 18, 24 . . . . 42; multiples of 7 = 7, 14, 21, 28 . . . . 42) and choose the smallest multiple that is exactly divisible by 6 and 7, i.e., 42.

What are the Methods to Find LCM of 6 and 7?

The commonly used methods to find the LCM of 6 and 7 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 6 and 7 by Prime Factorization?

To find the LCM of 6 and 7 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (7 = 7). LCM of 6 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 7.
⇒ LCM of 6, 7 = 2¹ × 3¹ × 7¹ = 42.

What is the Relation Between GCF and LCM of 6, 7?

The following equation can be used to express the relation between GCF and LCM of 6 and 7, i.e. GCF × LCM = 6 × 7.

If the LCM of 7 and 6 is 42, Find its GCF.

LCM(7, 6) × GCF(7, 6) = 7 × 6
Since the LCM of 7 and 6 = 42
⇒ 42 × GCF(7, 6) = 42
Therefore, the GCF = 42/42 = 1.