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.

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1.LCM of 6 and 7
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 6 and 7 is 42.

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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 MethodBy Listing MultiplesBy Prime Factorization Method

LCM of 6 and 7 by Division Method

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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 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

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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.

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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.