a number of soilders when divided into groups of three,five or seven,will give a remainder of 2.

题目

a number of soilders when divided into groups of three,five or seven,will give a remainder of 2.
(a)what is the least number of soldiers?
(b)if there were about 3000 soldiers,then find its actual number.

答案

a.3,5,7的最小公倍数是105,余数为2,故105+2=107The least number of soldiers is 107b.3000/105 在28-29之间28x105+2=294229x105+2=30473047更接近3000,所以the actual number is 3047