SOLUTION: find the smallest positive integer value of m for which cube root of (180x784xm) is a whole number

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Question 969976: find the smallest positive integer value of m for which cube root of (180x784xm) is a whole number
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at the prime factors of each number,
180=2%2A2%2A3%2A3%2A5
784=2%2A2%2A2%2A2%2A7%2A7
So the twos are already in a multiple of 3, 2%5E6
The three needs 1 to make 3%5E3.
The five needs 2 to make 5%5E3.
The seven needs 1 to make 7%5E3.
m=3%2A5%2A5%2A7=highlight%28525%29