Question

Find the least number which when divided by 6,15,18 leave the remainder 5 in each case.

Answer 1

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.