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Question
What is the smallest number that, when divided by 35, 56 and 91 leaves remainders of 7 in each case?
Solution
TO FIND: Smallest number that, when divided by 35, 56 and 91 leaves remainder of 7 in each case
L.C.M OF 35, 56 and 91
`35= 5xx7`
`56=2^2xx7`
`91=13xx7`
L.C.M of 35,56 and 91 = `2^2xx5xx7xx13`
=3640
Hence 84 is the least number which exactly divides 28, 42 and 84 i.e. we will get a remainder of 0 in this case. But we need the smallest number that, when divided by 35, 56 and 91 leaves remainder of 7 in each case
Therefore
= 3640 +7
= 3647
Hence 3647 is smallest number that, when divided by 35, 56 and 91 leaves remainder of 7 in each case.
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