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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=2^2xx7`
`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
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