A temple has five bells which ring at intervals of 12, 15, 16, 20 and 25 minutes respectively. If they ring together at midnight, then at what time next will they ring together?

8 : 00 PM

L.C.M. of 12, 15, 16, 20 and 25

12 = 2 × 2 × 3

15 = 3 × 5

16 = 2 × 2 × 2 × 2

20 = 2 × 2 × 5

25 = 5 × 5

Hence, L.C.M. = 2⁴ × 3 × 5 × 5 = 1200 minutes = \(\frac{1200}{60}\)  = 20 hours

They will ring together again = 12 AM + 20 hours = 8 PM

∴ They will ring together again at 8 PM.