Question

Mrs. Canon and Mrs. Solace are both getting their nails done today. Mrs. Canon gets her nails done every 8 days. Mrs. Solace gets her nails done every 12 days. In how many days will they be at the nail salon on the same day again?

Answer 1

24

Step-by-step explanation:(LCM) 8,16,24

(LCM)12,24

LCM is 24 so the answer to the question is 24

Answer 2

24 days

Explanation:

The least common multiple (LCM) of 8 and 12 is 8·3 = 12·2 = 24.

The ladies will be at the nail salon on the same day again in 24 days.

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8 = 2³

12 = 2²·3

The LCM will have these factors to their highest powers: 2³·3 = 24.

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The LCM is also the product divided by their greatest common factor (GCF). GCF(8, 12) = 4, so ...

LCM(8, 12) = 8·12/4 = 24