Question

circular field has circumfrence of 360 km.three cyclists start together and can cycle 48,60and 72 km a day.when will they meet again

Answer 1

The job should calculate the least common multiple of numbers:
48, 60, 72, 360 (school method)

  48  /  2  =  24  / 2 = 12  / 2 =   6  /  2 =  3 / 3 = 1 / 3 = 1 / 5 = 1      
  60              30          15           15          15         5          5         1
  72              36          18             9            9          3          1         1
360            180          90          45           45       15          5         1

The least common multiple is  2 × 2 × 2 × 2 × 3 × 3 × 5 = 720 = 2 * 360
So, they meet again after 2 laps, because:
720 = 48 × 15 = 60 × 12 = 72 × 10