Question

Strand 1 changes color every 12 seconds strand 2 changes color every 13 seconds both strands just changed color. After how many seconds will the strands change color at the same time again

Answer 1

156 seconds

Explanation:

To find out when both strands will change color at the same time again, we need to find the least common multiple (LCM) of the two time intervals: 12 seconds and 13 seconds.

The LCM is the smallest positive number that is divisible by both 12 and 13 without a remainder.

To find the LCM, we can list the multiples of each number until we find a common multiple:

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, ...

Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, ...

From the lists above, we can see that the least common multiple (LCM) of 12 and 13 is 156.

Therefore, the strands will change color at the same time again after 156 seconds.