Question

Please solve this problem using HCF or LCM:
Sam and Carlos are bowling with plastic pins in Sam's living room. Remarkably, Sam knocks down 8 pins on every bowl and Carlos knocks down 9 pins on every bowl. At the end of the day, Sam and Carlos have knocked down the same total no of pins. What is the least no of total pins that Sam and Carlos could have *each* knocked down?

Plz show working and no guesses...

Answer 1

72 is the right answer

Answer 2

Given :

Sam knocks down 8 pins on every bowl and Carlos knocks down 9 pins on every bowl. At the end of the day, both have knocked down the same total no. of pins.

To Find :

The least no. of total pins that Sam and Carlos could have each knocked down.

Solution :

We will calculate LCM (Lowest Common Multiple) of the numbers 8 and 9.

1  | 8, 9

8 | 8, 9

9 | 1, 9

   | 1, 1  

Prime factors of 8,9 = 1 × 8 × 9

LCM of 8, 9 = 72

The least no of total pins that both could have each knocked down would be 72 pins.