Lots of divisors

Number Theory Level 2

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


The answer is 2520.

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Jack Sacks by Jack Sacks , 18, United Kingdom

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1 solution

Kay Xspre
Feb 14, 2016

Notice that 2 , 3 , 4 , 6 2, 3, 4, 6 is divisible by 8 × 9 8\times 9 , 10 is divisible by 2 × 5 2\times 5 , and 2 divided 8. We then pick only 8 × 9 × 7 × 5 = 2520 8 × 9 ×7 ×5 = 2520 as our answer

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes! It can be generalized as the products of highest powers of primes less than n n . In case of 10, it is 2 3 ⋅ 3 2 ⋅ 5 ⋅ 7 2^3 \cdot 3^2 \cdot 5 \cdot 7 .

Arulx Z - 5 years, 3 months ago

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