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Question

Find the least number which when divided by 15,20,35,45 leaves remainder 5 in each case

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Solution

To find the least number which when divided by 15,20,35 and 45 gives remainder 5, we first have to find the least common multiple of 15,20,35 and 45.

LCM of 15,20,35,45 = LCM(15,20,35,45)

= 1260

So the number 1260 is the smallest number divisible by all 15,20,35 and 45.
So if we add 5 to 1260, i.e. 1260+5=1265, we get the smallest number which when divided by 15,20,35 and 45 would give a remainder 5, in each case.

So the required answer is 1265.

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