Question

Find the least number which when divided by 9, 15 ,18 leaves remainder 7 in each case explain

Answer 1

To find the least number which when divided by 9, 15 and 18 leaves a remainder 7 in each case, we have to find the L.C.M. of 9, 15 and 18 and then add 7 in that number.

L.C.M. of 9, 5 and 18

9 = 3×3
15 = 3×5
18 = 2×3×3

L.C.M. of 9, 15 and 18 = 2*3*3*5 = 90

Now,
7+ 90 = 97

Hence, 97is the least number which when divided by 9, 15 and 18 leaves a remainder 7 in each case.

Let us check our answer.

1) 97/9
Quotient = 10
Remainder = 7

2) 97/15
Quotient = 6
Remainder = 7

3) 97/18
Quotient = 5
Remainder = 7

So, the required number is 97.