Question

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

Answer 1

TO FIND: The smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively. 

L.C.M of 28 and 32.

`28=2^2xx7`

`32=2^5`

L.C.M of 28 and `32= 2^5xx7`

= 224 

Hence 224 is the least number which exactly divides 28 and 32 i.e. we will get a remainder of 0 in this case. But we need the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively 

Therefore

= 224 – 8 – 12

= 204

Hence 204 is the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.