If Kate sang a note every 2 seconds and Gaby sang a note every 6 seconds and Laney sang a note every 16 seconds, how often would they all sing at the same time?

What is the least common multiple of 2, 6, and 16?

Hint: What is the smallest number that is evenly divisible by 2 and 6?

16, 32, 48, 64, 80

How do I write 5/16ths as a decimal??

Divide 5 by 16.

Thank you so much!!

You're very welcome.

To find out how often Kate, Gaby, and Laney would all sing at the same time, we need to find the time it takes for their singing patterns to sync up.

First, let's find the time it takes for Kate, Gaby, and Laney to individually sing one note.
Kate sings a note every 2 seconds, Gaby sings a note every 6 seconds, and Laney sings a note every 16 seconds.

The time it takes for each of them to sing a note simultaneously will be the least common multiple (LCM) of 2, 6, and 16.

To calculate the LCM, we can follow these steps:
1. Find the prime factors of each number:
- Prime factors of 2: 2
- Prime factors of 6: 2, 3
- Prime factors of 16: 2, 2, 2, 2 (or 2^4)

2. Multiply each prime factor the greatest number of times it occurs in any of the given numbers:
- LCM = 2^4 * 3 = 48

Therefore, Kate, Gaby, and Laney would all sing at the same time every 48 seconds.