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?

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

Step-by-step 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.

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step-by-step explanation: