Problems on H.C.F and L.C.M
The traffic lights at three different road crossings change after every 48 sec., 72 sec and 108 sec.respectively .If they all change simultaneously at 8:20:00 hours,then at what time they again change
Interval of change = (L.C.M of 48,72,108)sec.=432sec. So, the lights will agin change simultaneously after every 432 seconds i.e,7 min.12sec Hence , next simultaneous change will take place at 8:27:12 hrs.
Let the numbers be 37a and 37b.Then, 37a x 37b = 4107 ab = 3.Now, co-primes with product 3 are (1, 3).So, the required numbers are (37 x 1, 37 x 3) i.e., (37, 111). Greater number = 111.
LCM of 2, 3, 4 and 5 is 60.The smallest number of two digits is 10.But we also see that the smallest number divisible by 2, 3, 4 and 5 is 60. Therefore, 10 has no significance here.The difference between divisor and remainder is 2 in each case. So, we subtract 2 from 60.60 - 2 = 58
EXAMIANS