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

The required number is determine with the help of LCM of 28 and 32.

Using prime factorization , Find the LCM

$28=2\times 2\times 7$
$32=2\times 2\times 2\times 2\times 2$

LCM = 224
Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 is 224 -(8 +12) = 204