division problem

Question

if you divide it by 2, 3, 4, 5, or 6 you will geta remainder of 1.  If you divide it by 11, the remainder is 0. What number is this?  How do I figure that out?

Answer 1

The number will be 1 more than the least common multiple of 2, 3, 4, 5, and 6.  We find the least common multiple by factoring each number down to their primes:

 

2:  1,2

3:  1,3

4:  1,2,2

5:  1,5

6:  1,2,3

 

Ignoring the ones, we need 2x2x3x5 which is 60.  So the number is 61, which will divide by 2, 3, 4, 5, or 6 and leave a remainder of 1.  But 61÷11 is 5 with a remainder of 6, so we must try the next multiple of 60, which is 120.  121 will leave a remainder of 1 when divided by 2, 3, 4, 5, or 6, and it is evenly divisible by 11.