Question

A committee of three students met with the principal today and agreed that Rachel will report to the principal every $9$ days, Jessica every $12$ days, and Richard every $15$ days. What is the least number of days before all three will again report to the principal on the same day?

Answer 1

180 days

Explanation:

To solve for the least number of days all three will again be report to the principal, find the lowest common multiples of all three of them

Rachel will report to the principal every 9 days, Jessica every 12 days, and Richard every 15 days

Rachel (every 9 days) = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

Jessica (every 12 days) = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180

Richard (every 15 days) = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180

The lowest common multiples of 9 days, 12 days, 15 days is 180 days

Therefore, the least number of days all three will report again to the principal is 180 days