Which steps would I have to make to solve this. Thank you

Question

One nurse is instructed to check a patients blood pressure every 45 minutes and another is instructed to take the same patients every 60 minutes. If both nurses are in the patients room at this time, how long with it be until the nurses are in the same room together again?

Answer 1

3 hours

leas common multiple of 45 and 60 is 180

in 180 minutes they'll both be in the same room again

180/45 = 4th time one nurse is back

180/60 = 3rd time the other nurse is back

in 3 hours they'll run into each other again

45 = 9x5 = 3x3x5

60 = 3x4x5

120 = 3x3x5x4

you need to multiply enough prime factors from each 45 and 60 together to include every prime factor in both but no more.