Question

Find the least number which when divided by 16, 36 and 40 leaves 5 as remainder in
each case.​

Answer 1

Answer:

The answer to this one is 5 more than the LCM of 16, 36 and 40. To find the LCM, break down each of the numbers into its prime factors. Thus 16 = 2 x 2 x 2 x 2, so the LCM will have to have at least four factors of 2; similarly, 36 = 2 x 2 x 3 x 3 and 40 = 2 x 2 x 2 x 5, so the LCM will also have to have at least two factors of 3 and a single 5. Gathering the necessary factors, we get the LCM of 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720. Adding 5 (the remainder from each division), we get 725. Checking, 725 = (16 x 45) + 5 = (36 x 20) + 5 = (40 x 30) + 5.

Answer 2

Answer:

725

Step-by-step explanation:

First we have to find the LCM of 16, 36 and 40.

To find the LCM, we have to find the prime factors.

Thus 16 = 2 x 2 x 2 x 2,

LCM will have to have at least four factors of 2; similarly,

36 = 2 x 2 x 3 x 3 and 40 = 2 x 2 x 2 x 5,

Therefore LCM will also have to have at least two factors of 3 and a single 5.

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720.

Adding 5 (the remainder from each division), we get 725.

Checking, 725 = (16 x 45) + 5 = (36 x 20) + 5 = (40 x 30) + 5.