SOLUTION: boxes that are 120cm tall are being stacked next to boxes that are 90cm tall. what is the shortest possible height at which the two stocks will be level with one another?

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Question 1014544: boxes that are 120cm tall are being stacked next to boxes that are 90cm tall. what is the shortest possible height at which the two stocks will be level with one another?

Found 2 solutions by FrankM, macston:
Answer by FrankM(1040) (Show Source):
You can put this solution on YOUR website!
You are looking for the least common multiple.
Think of it this way - 120 = 4 * 30, and 90 = 3 *30.
4 and 3 are primes and their LCM is simply 12, or 4*3.
So we need 3 * 120 = 360 and 4 * 90 = 360 to get the number you seek.

Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
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Find the prime factors:
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120 = 2 x 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
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Choose the most often repeated number of each factor:
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2 is repeated 3 times in 120
3 is repeated 2 times in 90
Five only occurs once at most.
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We have 3-2s, 2-3s, and 1-5
2 x 2 x 2 x 3 x 3 x 5 =360
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ANSWER: 360 cm is the lowest height both will be equal.
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