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

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