Question

Drusilla replaces the light bulb in the hall every 9 months and the air filter every 6 mont. she just replaced bot this month. After how many months will she replace both again?

Answer 1

Answer: Drusilla will replace both again after 18 months.

Explanation: If Drusilla replaced both the light bulb and the air filter in September 2019, she will replace both again in March 2021, which means she will replace them together after 18 months (a year and a half). What explains this result is the fact that the least common multiple of 9 and 6, that is to say the smallest multiple of these two numbers, is 18. Therefore, the correct answer is 18 months.

Answer 2

The least common multiple of 9 and 6 is 18 so in 18 months she will replace the bulb for the 2nd time and the air filter for the 3rd time. It will be the first time they are replaced together.