Two cyclists start together at the same point of a velodrome track in Indore. One completes a lap in 39 seconds and the other in 52 seconds.
After how long do they meet again at the starting point, and how many laps has the faster cyclist completed by then?

They meet at the start after LCM(39, 52) seconds. $39=3\times 13$ and $52=2^2\times$ 13, so LCM = $2^2\times 3\times 13=156$ s. The faster cyclist takes 39 s per lap, so he has done 156 / 39 = 4 laps. Using the HCF, 13 s, describes no meeting at all; $39\times 52=2028$ over-counts because the lap times are not co-prime; dividing 156 by 52 gives the slower cyclist's 3 laps.