need to find out when they will start swimming together again

Question

Tom swims one lap every 5 minutes. Rob swims one lap every 4 minutes. If they start together, in how many minutes will they start together again?

Answer 1

The Least Common Multiple of two numbers may be found by:

 

[1] List the multiple of the numbers and select the lowest (least) value in both lists (in common):

 Multiples of 5:     0     5     10     15     20     25     30     35      [times Tom passes Start]

 Multiples of 4:     0     4     8       12     16     20     24     28      [times Rob passes Start]

 

LCM = 20

 

 

[2] List the prime factors of each number and select the smallest set that includes all prime factors:

  Prime Factors of 5:         5

  Prime Factors of 4:         2*2

      LCM = 2*2*5 = 20