Question

What is the smallest 4-digit positive number divisible by 2, 3, 4, 5, 6, 8, 9, and 10?

Answer 1

Answer: 1080

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Explanation:

let's find the prime factorization for each value. If the value is prime, then just move onto the next value

2 = 2 ... already prime, nothing needed to do here

3 = 3

4 = 2*2

5 = 5

6 = 2*3

8 = 2*2*2

9 = 3*3

10 = 2*5

The list of prime factors that show up are: {2, 3, 5}

We have '2' show up at most 3 times, the prime '3' show up at most 2 times, and the prime '5' show up at most 1 time.

This means 2^3*3^2*5 = 360 is the LCM of the list {2,3,4,5,6,8,9,10}

Any multiple of 360 will also be a common multiple of the original list of values.

Multiples of 360: {360, 720, 1080, ...}

We see that 1080 is the smallest 4-digit multiple of 360.