Question

You hang two strings of decorative lights. Strand 1: changes between red and blue every 15 seconds. Strand 2: changes between green and gold every 18 seconds. Both strands just changed color. After how many seconds will the strands change color at the same time again?

Answer 1

The strands change color at the same time again after 90 seconds

Explanation:

We are told:

Strand 1: changes between red and blue every 15 seconds.

Strand 2: changes between green and gold every 18 seconds.

To solve for this question, we use the LCM method.

Step 1

List multiples of each number until the first common multiple is found.

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120

Multiples of 18:

18, 36, 54, 72, 90, 108, 126

Therefore,

LCM(15, 18) = 90

The first common multiple is 90, and this is the lowest common multiple.

Therefore, the strands will change color at the same time again after 90 seconds.