Question 730868: candies are packed in four different sized packets containing 200, 300, 450 or 600 candies respectively. find the smallest number of candies needed to make an exact number of packets of each size. also, find the number of packets, of each kind, that will be made from this number.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A number of candies that would make an exact number of packets for all those packet sizes must be a multiple of 200, 300, 450 and 600.
The least common multiple of those numbers is 
If you look at multiples of 600, you notice that:
600 will not work, because it is not a multiple of 450,
2 x 600 = 1200 does not work either, because it is not a multiple of 450,
but the next multiple of 600 works, because
3 x 600 = 1800 = 4 x 450 is a multiple of 450.
Another way of figuring out the least common multiple involves using the prime factorization of the numbers. If you were not taught that, feel free to ignore what follows.
A common multiple has to have at least as many of each prime factor as all the numbers.
So we need to include 2 as a factor 3 times ( ) .
We also need to include 3 twice ( )
and 5 twice ( ) .
The least common multiple, including all those factors, is
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