What is the smallest whole number that can be divided by any number from 1 to 20 (inclusive) and not leave a remainder? For example, 60 is the smallest number that can be divided evenly by all the numbers from 1 – 5.

Note: This problem can be solved in only a couple of minutes using only pen and paper.

There are different ways to come to this answer, but the simplest is as follows.

For each number from 1 to 20 find their prime factors as follows.

1 = 1
2 = 2
3 = 3
4 = 2 × 2
5 = 5
6 = 2 × 3
7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
11 = 11
12 = 2 × 2 × 3
13 = 13
14 = 2 × 7
15 = 3 × 5
16 = 2 × 2 × 2 × 2
17 = 17
18 = 2 × 3 × 3
19 = 19
20 = 2 × 2 × 5

Once you’ve done this, make a list of all the prime numbers you would need to make any number from 1 – 20. This list would be

1, 2, 2, 2, 2, 3, 3, 5, 7, 11, 13, 17,19

Multiply these numbers together gives you 232792560.

On a smaller scale, to find the the smallest number that can be divided evenly by 1 – 5.

1 = 1
2 = 2
3 = 3
4 = 2 × 2
5 = 5

1 × 2 × 2 × 3 × 5 = 60