Question

Find the smallest 5 digit number exactly divisible by 6, 7, 8, 9and 10.​

Answer 1

Step-by-step explanation:

List all prime factors for each number.

Prime Factorization of 6 is:

2 x 3 => 21 x 31

Prime Factorization of 7 shows:

7 is prime => 71

Prime Factorization of 8 is:

2 x 2 x 2 => 23

Prime Factorization of 9 is:

3 x 3 => 32

Prime Factorization of 10 is:

2 x 5 => 21 x 51

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 2, 3, 3, 5, 7

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520

In exponential form:

LCM = 23 x 32 x 51 x 71 = 2520

LCM = 2520

Therefore,

LCM(6, 7, 8, 9, 10) = 2520

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