A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?
Q1. A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?
Answer: 7203
Explanation: LCM(16, 20, 25, 45) = 3600; number = 3600k + 3 must be divisible by 21; 3600k + 3 ≡ 0 (mod 21); since 3600 mod 21 = 9, we need 9k ≡ 18 (mod 21), giving k = 2; number = 7203.