Question

Peter noticed that his house# is divisible by both 72 and 112.

1) What's the smallest integer that his house number could be?

2) If the house number is between 3000 and 4000, what's the house number?

Answer 1

1. 1008
2. 3024

Explanation:

1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.

The least common multiple of 72 and 112 is 1008.

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2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...

3 × 1008 = 3024

Peter's house number is 3024.