Machines a and t were both cleaned this week machine a is cleaned every 12 weeks and machine t is cleaned every 8 weeks what is the fewest number of weeks that will pass before both machines are cleaned again in the same week. show work lcm

The fewest number of weeks that will pass before both machines are cleaned again in the same week is 24 weeks.

Step-by-step explanation:

Given : Machines a and t were both cleaned this week machine a is cleaned every 12 weeks and machine t is cleaned every 8 weeks.

To find : What is the fewest number of weeks that will pass before both machines are cleaned again in the same week ?

Solution :

According to question,

We have take LCM of the numbers 12 and 8.

2 | 8  12

2 | 4   6

2 | 2   3

3 | 1   3

  | 1   1

Therefore, the fewest number of weeks that will pass before both machines are cleaned again in the same week is 24 weeks.

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step-by-step explanation:

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