EGYPTIAN DIVISIBILITY !

A group of Archaeologists discovered some simple hieroglyphs on the stone lid of a tomb in Egypt. When they translated them they realized that it was a four digit number, but more remarkably it is the smallest number that can be divided by all of the numbers from 1 to 10 without any remainder. What was that number?


The answer is 2520.

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2 solutions

Putting the numbers as under:-
1,~~ 2^1,~~3^1,~~2^2,~~5^1,~~2^1*3^1,~~7^1,~~2^3,~~3^2, ~~2^1*5^1, \\\text{ We see that the primes appearing are,'' 2, 3 5 7'' their product with}\\\text{ highest power= 2^3*3^2*5^1*7^1 = } \boxed{\color{#D61F06}{2520} }

Nihar Mahajan
Jan 31, 2015

By considering the prime factors of each of the numbers from 1 to 10:

2 = 2 , 3 = 3 , 4 = 2x2 , 5 = 5 , 6 = 2x3 , 7 = 7 , 8 = 2x2x2 , 9 = 3x3 , 10 = 2x5 .

We can deduce that the smallest number which evenly divides 2, 3, 4, ... , 10, must be 2x3x2x5x7x2x3 = 2520.

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