Minimising Divisibility

Number Theory Level 1

What is the smallest positive integer that is divisible by 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 10 ?


The answer is 2520.

Daniel Hinds by Daniel Hinds , 20, United Kingdom

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1 solution

Chew-Seong Cheong
Mar 21, 2020

The problem is equivalent to finding the lowest common multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

lcm ( 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ) = 2 3 × 3 2 × 5 × 7 = 2520 \text{lcm }(1, 2, 3, 4, 5, 6, 7, 8, 9, 10) = 2^3 \times 3^2 \times 5 \times 7 = \boxed{2520}

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