The first six
What is the smallest positive integer that is divisible by each of the first six positive integers?
The answer is 60.
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2 solutions
Moderator note:
Simple standard approach.
How does this number grow as we increase the number of initial positive integers that divide it?
The first six positive integers are 1, 2, 3, 4, 5 and 6.
Any positive integer is divisible by 1.
if a number is divisible by 4, it is also divisible by 2.
If a number is divisible by 2 and by 3, it is also divisible by 6.
So we need a number divisible by 3, 4 and 5, which are mutually coprime. The smallest such number is 3 * 4 * 5 = 60.