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Divide 1 to 20

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.

232792560

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

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over 1 year ago
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Difficulty 5.0 ?

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