Question

Determine the largest four digit numner divisible by 18, 25, and 35

Answer 1

You can find the LCM using prime factors as follows:18 = 2 x 3 x 3 = 2^1*∗3^2,25 = 5 x 5 = 5^2,35 = 5 x 7 = 5^1*7^1,So any number divisible by 18, 25 and 35 needs a 2, two 3s, two 5s and a 7 among its factors.

This means that it has to be divisible by 2*3*3*5*5*7 =3,150.So we need to find the highest multiple of 3,150 less than 10,000.This would be 3*3,150 = 9,450