SOLUTION: Today,you took your car to have the tires rotated and to have the windshield wiper blades replaced. You have your tires rotated every six months and you replace the windshield wipe

Question 370485: Today,you took your car to have the tires rotated and to have the windshield wiper blades replaced. You have your tires rotated every six months and you replace the windshield wiper blades every eight months. In how many months will you next rotate the tires and replace the windshield wiper blades on the same day?
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Today,you took your car to have the tires rotated and to have the windshield wiper blades replaced. You have your tires rotated every six months and you replace the windshield wiper blades every eight months. In how many months will you next rotate the tires and replace the windshield wiper blades on the same day?
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The least common multiple of 6 months and 8 months is 24months.
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Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The two events will occur every 'n' months where 'n' is the LCM of 6 and 8. Since the LCM of 6 and 8 is 24, this means that the two events will happen on the same day 24 months from now (ie 2 years from now)

How did I know that the LCM of 6 and 8 is 24? First I found the GCF of 6 and 8 to be 2 (since this is the largest factor that they share in common). Then I multiplied 6 and 8 to get 48 and then finally divided by 2 to get 24.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
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