Question

Which is the smallest number that is a perfect square which can be divided by 14, 24, 35 and 77? PLEASE TELL WITH FULL WORKING

Answer 1

853776

Explanation:

First we need to find the least common multiple of these 4 numbers.

Factoring the numbers, we have:

14 = 2 * 7

24 = 2 * 2 * 2 * 3

35 = 3 * 7

77 = 7 * 11

The LCM will be 2 * 2 * 2 * 3 * 7 * 11 = 1848

Then, we need a perfect square number, so we need a number where each prime factor appears an even number of times, so the smallest number we can get is:

2 * 2 * 2 * 2 * 3 * 3 * 7 * 7 * 11 * 11 = 853776