number game

Number Theory Level 2

What is the smallest positive number which can be divided by 1,2,3....up to 10?


The answer is 2520.

Dhruvil Darji by Dhruvil Darji , 26, India

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1 solution

Karthik Sharma
Jul 16, 2014

Smallest number which can be divided by 1,2,3,4,5,6,7,8,9 and 10 = L.C.M. ( 1,2,3,4,5,6,7,8,9,10) = 2520 \text{L.C.M. ( 1,2,3,4,5,6,7,8,9,10) = 2520}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Compute the prime factors of each of the factors:

1 = 1

2 = 2

3 = 3

4 = 2*2

5 = 5

6 = 2*3

7 = 7

8 = 2 2 2

9 = 3*3

To get our least common multiple, combine the highest powers of all the primes. For the 2's, that is 2 2 2. For the 3's, that would be 3 3. We also have one each of a 5 and a 7. The least common multiple is the product of all these, which is 2 2 2 3 3 5*7 = 2520

Fares Salem - 6 years, 8 months ago

Thanks, I've updated the wording of the question to "can be divided by", instead of "which divides".

Calvin Lin Staff - 6 years, 10 months ago

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