Alvin, Calvin and Melvin are running laps around a track. Alvin runs a lap every 4 minutes, Calvin runs a lap every 6 minutes and Melvin runs a lap every 9 minutes. If they start off at the same point, how many minutes will it take before all three of them are back at the starting point?

36 4x6x9= 216 mins

To determine how many minutes it will take before all three of them are back at the starting point, we need to find the least common multiple (LCM) of their lap times.

The LCM is the smallest positive integer that is divisible by all the given numbers. We can find the LCM by finding the prime factorization of each number.

The prime factorization of 4 is 2 × 2.
The prime factorization of 6 is 2 × 3.
The prime factorization of 9 is 3 × 3.

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers:

2 (from 2 × 2)
3 (from 3 × 3)

Multiplying these prime factors together, we get: 2 × 2 × 3 × 3 = 36.

Therefore, it will take 36 minutes before all three of them are back at the starting point.