What is the greatest number less than 10000, which is exactly divisible by 48, 60 and 64?
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M$2 Answers
48 = 2*2*2*2*3
60 = 2*2*5*3
64 = 2*2*2*2*2*2
to get the least common multiple you take the greatest power of each factor and multiply them together
the greatest power of 2 is 2*2*2*2*2*2
the greatest power of 3 is 3
the greatest power of 5 is 5
so the LCM is 2*2*2*2*2*2*3*5 = 960
the multiples of 960 that are less than 10000 are 960, 1920, 2880, 3840, 4800, 5760, 6720, 7680, 8640, 9600
So the final answer to this problem is 9600
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M$9600 = 60 x 160
9600 = 64 x 150
The proof will take a while to type, but the sequence is:
Prime factorize 48, 60, and 64
Find the least common multiple = M
Divide 10,000 by that multiple = x
take integer part of the answer = y
Multiply y by M
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M$
