Three traffic signals on a road change every 48 s, 72 s and 108 s. They all change together at 7:00:00 am. At what time will they next change together?

7:07:12 amCorrect answerYour answer7:03:36 amCorrect answerYour answer7:02:24 amCorrect answerYour answer7:14:24 amCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

They change together after LCM(48, 72, 108) seconds.
$48 = 2^4 \times 3$ , $72 = 2^3 \times 3^2$ , $108 = 2^2 \times 3^3$ , so LCM = $2^4 \times 3^3 = 432$ s.
432 $s = 7$ min 12 s, so the time is 7:07:12 am.

Worth noting

7:02:24 am uses $\operatorname{LCM}(48, 72) = 144$ s and 7:03:36 am uses $\operatorname{LCM}(72, 108) = 216$ s, ignoring one signal.

Ten questions from HCF & LCM, at your own pace.

Explanation