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1. On a road three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 AM sharp, at what time will they change simultaneously?
36 = 2 × 2 × 3 × 3
42 = 2 × 3 × 7
72 = 2 × 2 × 2 × 3 × 3
LCM = 2 ×2 × 2 × 3 × 3 × 7 = 504 seconds.
LCM of 36, 42 and 72 is 504
Hence, the lights will change simultaneously after 8 minutes and 24 seconds.
Solution:
LCM of 36, 42 and 72,36 = 2 × 2 × 3 × 3
42 = 2 × 3 × 7
72 = 2 × 2 × 2 × 3 × 3
LCM = 2 ×2 × 2 × 3 × 3 × 7 = 504 seconds.
LCM of 36, 42 and 72 is 504
Hence, the lights will change simultaneously after 8 minutes and 24 seconds.