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

You are watching: Least common multiple of 6 and 7

1. | LCM the 6 and also 7 |

2. | List the Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM of 6 and 7 is 42.

**Explanation: **

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

The methods to discover the LCM of 6 and also 7 are defined below.

By department MethodBy Listing MultiplesBy element Factorization Method### LCM of 6 and also 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 determinants (preferably common). The product of these divisors gives the LCM of 6 and also 7.

**Step 3:**continue the measures until just 1s room left in the critical row.

The LCM that 6 and also 7 is the product of every prime number on the left, i.e. LCM(6, 7) by division method = 2 × 3 × 7 = 42.

### LCM that 6 and also 7 by Listing Multiples

To calculation the LCM of 6 and 7 by listing out the usual multiples, we have the right to 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 native the multiples the 6 and also 7 are 42, 84, . . .

**Step 3:**The smallest usual multiple the 6 and 7 is 42.

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

See more: Optional Arguments Are Always Placed First In The Argument List.

### LCM the 6 and 7 by prime Factorization

Prime administrate of 6 and also 7 is (2 × 3) = 21 × 31 and also (7) = 71 respectively. LCM that 6 and 7 deserve to be derived by multiplying prime components raised to their respective greatest power, i.e. 21 × 31 × 71 = 42.Hence, the LCM that 6 and 7 by prime factorization is 42.