Question

5. Find the smallest number which leaves the remainder 8 and 12 when divided by 28 and 32 respectively.​

Answer 1

Solution:

First, find the LCM of 28 and 32 which is 224.

Using the remainder rule:

dividend = divisor*quotient + remainder

224 = 28 * 8 - No remainder.

But

224 = 216 + 8 -Because you want R = 8

224 = 28 * 7 = (196 + 20) + 8

224 - 20 = 28 * 7 + 8 .... 1

Similarly

224 = 32 * 7 = 0

But

224 = 212 + 12 -Because you want R = 12

224 = 32 * 6 = (192 + 20) + 12

224 - 20 = 32 * 6 + 12 .... 2

Therefore, the smallest dividend = 224 - 20 = 204

To check:

204 divided by 28, remainder = 8

204 divided by 32, remainder = 12

Hope this will help.