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The traffic lights at three different road crossings change after every $45$ seconds, $75$ seconds and $60$ seconds respectively. If they change together at $5.00$ a.m., then at what time they will change together next?
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Solution: $45 = 3^2 \times 5, 75 = 3 \times 5^2, 60 = 2^2 \times 3 \times 5$
$LCM (45, 75, 60) = 2^2 \times 3^2 \times 5^2 = 900$
$900$ seconds $= 15$ minutes
Lights will change together at $5:15$ a.m. again
$LCM (45, 75, 60) = 2^2 \times 3^2 \times 5^2 = 900$
$900$ seconds $= 15$ minutes
Lights will change together at $5:15$ a.m. again