Find the smallest no such that when it is divided by 28,38,63 leaves r

1.	Find the smallest no such that when it is divided by 28,38,63 leaves remainder 18,28,38 respectively
Answer» Given that the smallest number when divided by 28 and 32 leaves REMAINDER 8 and 12 respectively. 28 - 8 = 20 and 32 - 12 = 20 are divisible by the REQUIRED numbers. Therefore the required number will be 20 less than the LCM of 28 and 32. Prime FACTORIZATION of 28 = 2 * 2 * 7 Prime factorization of 32 = 2 * 2 * 2 * 2 * 2 LCM(28,32) = 2 * 2 * 2 * 2 * 2 * 7 = 224. Therefore the required smallest number = 224 - 20 = 204. Verification: 204/28 = 28 * 7 = 196. = 204 - 196 = 8 204/32 = 32 * 6 = 192 = 204 - 192 = 12.

Find the smallest no such that when it is divided by 28,38,63 leaves remainder 18,28,38 respectively

Answer»

Given that the smallest number when divided by 28 and 32 leaves REMAINDER 8 and 12 respectively.

28 - 8 = 20 and 32 - 12 = 20 are divisible by the REQUIRED numbers.

Therefore the required number will be 20 less than the LCM of 28 and 32.

Prime FACTORIZATION of 28 = 2 * 2 * 7

Prime factorization of 32 = 2 * 2 * 2 * 2 * 2

LCM(28,32) = 2 * 2 * 2 * 2 * 2 * 7

= 224.

Therefore the required smallest number = 224 - 20

= 204.

Verification:

204/28 = 28 * 7 = 196.

= 204 - 196

= 8

204/32 = 32 * 6 = 192

= 204 - 192

= 12.