LCM of 6 and 10 is the smallest number among all common multiples of 6 and 10. The first few multiples of 6 and 10 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 10 - by listing multiples, by prime factorization, and by division method.

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 1 LCM of 6 and 10 2 List of Methods 3 Solved Examples 4 FAQs

Answer: LCM of 6 and 10 is 30. Explanation:

The LCM of two non-zero integers, x(6) and y(10), is the smallest positive integer m(30) that is divisible by both x(6) and y(10) without any remainder.

The methods to find the LCM of 6 and 10 are explained below.

By Division MethodBy Listing MultiplesBy Prime Factorization Method

### LCM of 6 and 10 by Division Method

To calculate the LCM of 6 and 10 by the division method, we will divide the numbers(6, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 10.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 6 and 10 is the product of all prime numbers on the left, i.e. LCM(6, 10) by division method = 2 × 3 × 5 = 30.

### LCM of 6 and 10 by Listing Multiples To calculate the LCM of 6 and 10 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, 42, . . . ) and 10 (10, 20, 30, 40, . . . . )Step 2: The common multiples from the multiples of 6 and 10 are 30, 60, . . .Step 3: The smallest common multiple of 6 and 10 is 30.

∴ The least common multiple of 6 and 10 = 30.

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### LCM of 6 and 10 by Prime Factorization

Prime factorization of 6 and 10 is (2 × 3) = 21 × 31 and (2 × 5) = 21 × 51 respectively. LCM of 6 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.Hence, the LCM of 6 and 10 by prime factorization is 30.