Question

what is the smallest multiple of 11 that when divided by 2,3,4,5 or 6 has a remainder of 1

Answer 1

The lowest common multiple of 2, 3, 4, 5 and 6 is 60. What we're looking for is a solution to 11x=60y+1. If we divide this equation by 11 and write down the remainders only we get: 5y+1=0 or 5y=10, because 11-1=10. So y=2. Therefore 11x=60*2+1 and x=11. Each of the numbers divides into 121 with 1 as a remainder. The lowest multiple of 11 is 11. 2*60+1=3*40+1=4*30+1=5*24+1=6*20+1=11*11.