Question

Find the least number that when divided by

60. 120 and 180 leaves a remainder 5 in each case.
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Answer 1

Solution :-

To find the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case, we have to find the L.C.M. of 6, 15 and 18 and then add 5 in that number.

L.C.M. of 6, 5 and 18

6 = 2*3

15 = 3*5

18 = 2*3*3

L.C.M. of 6, 15 and 18 = 2*3*3*5 = 90

Now,

5 + 90 = 95

Hence, 95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.

Let us check our answer.

1) 95/6

Quotient = 15

Remainder = 5

2) 95/15

Quotient = 6

Remainder = 5

3) 95/18

Quotient = 5

Remainder = 5

So, the required number is 95.

Answer.

Explanation: