Three athletes Kayden, Chander and Karin start a race around a circular field. They take 90 seconds, 120 seconds and 150 seconds respectively to complete around. Find the time they will be at the same point if they started the race at 7:15 a.m.
Prime factorizations 90 = 2×3^2×5 (4 prime factors, 3 distinct) 120 = 2^3×3×5 (5 prime factors, 3 distinct) 150 = 2×3×5^2 (4 prime factors, 3 distinct)
LCM==2^3 x 3^2 x 5^2==1800 seconds 1,800 / 3,600 ==1/2 an hour after 7:15 or at 7:45 when all 3 will be at the same point.
