Question

The children from a football club are put into rows in the sports hall. When put into rows of 9 children, there are 2 children left over when put into rows of 12 children there are 2 children left over. What is the least number of childen in this football club

Answer 1

We are told that the children from a football club are put into rows in the sports hall. When put into rows of 9 children there are 2 children left over. When put into rows of 12 children there are 2 children left over.

We will find least number of children in football club by finding LCM of 9 and 12.

Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63,...

Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,...

We can see that least common multiple of 9 and 12 is 36.

We are told that 2 children left over from putting them into 9 and 12 children per row. To find least number we will add 2 to 36.

$9\cdot4+2=36+2=38$

$12\cdot3+2=36+2=38$      

$\text{Least number of children in football club}=36+2=38$

Therefore, the least number of children in the football club is 38.