Question

find the smallest number which when divided by 16, 50, 84 leave remainder 5 in each case,​

Answer 1

Answer:

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What is the smallest number which when divided by 16,28 and 40 leaves a remainder of 5 in each case?

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8 Answers



Aritra Chakraborty

, Consultant (2014-present)

Answered 2 years ago

Let’s see straight through it…. All three numbers will only divide a number when all of them are factors of it. So it’s obvious we need to find the LCM.

16 = 2^4

28 = 2^2 X 7

40 = 2^3 X 5

LCM = 2^4 X 7 X 5 (Taking the highest power of the nos.)

LCM = 560

So 560 Is the smallest number which the above three nos divide . But what is requested is that the smallest number which leaves the remainder 5.

So if we increase 5 from 560 , everytime these three nos will leave a remainder as 5. (Isn’t that obvious) :)

Hence the no. will be 560+ 5 = 565