Question:
Find the smallest number which leaves remainders 8 and 12 when divided by 28 and 32 respectively.
Solution:
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.
$28=2^{2} \times 7$
$32=2^{5}$
L.C.M of 28 , and $32=2^{5} \times 7$
$=224$
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