Question 1005689: three whole numbers have capacities of 24,56 and 120 litres. What is the volume of the largest container that can be used to fill each of them an exact number of times?
Found 2 solutions by Alan3354, bustod:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! three whole numbers have capacities of 24,56 and 120 litres. What is the volume of the largest container that can be used to fill each of them an exact number of times?
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There is no largest container.
If you mean smallest, it's the LCM, the Least Common Multiple of 24, 56 & 120.
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You can find that by factoring each of the 3 capacities, then using the highest power of each prime factor.
24 = 2*2*2*3
56 = 2*2*2*7
etc.
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But, 120 = 24*5, so the 24 can be ignored. 120 has all the factors except the 7.
--> 7*120 = 840 liters
Answer by bustod(2)  (Show Source):
You can put this solution on YOUR website! The answer is, a container of 8 lit.
The 24 lit container will be filled in 3 times, the 56 lit. container in 7 times, and 120 lit. in 15 times.
For the largest container that can be used to fill them all, it has to be <24, and should provide an integer solution when 56 & 120 are divided as well, which 24 does not satisfy.
The top 2 largest containers that will fill 24 lit are 12 & 8 lit. Of these, 56/12 is not an integer but 56/8=3 is, and so is 120/8=15.
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