The given five signals light up automatically at intervals of 3 min 4 minutes 8 min 10 min and 12 mi...........

Quantitative Aptitude ( CCS) LCM, HCF

The given five signals light up automatically at intervals of 3 min, 4 minutes, 8 min, 10 min, and 12 min respectively. How many times in 8 hours will they light up together from the time they start?

6 time

2 time

3 time

4 time

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Explanation:

We need the next instances when the signals light up.
That means the Least Common Multiple (LCM) of 3, 4, 8, 10, 12
3, 4 divide 12 so neglect them.
LCM of 8, 10 and 12
∴ LCM = 4 x 2 x 5 x 3 = 120 = They light up together after 2 hours
After starting, they light up together 1st time in 2 hours.
Then 2nd time in 2 + 2 = 4 hours.
Then 3rd time in 6 hours.
And 4th time in 8 hours.

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