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Question 624173: 1. Find the least perfect square number divisible by 3,4,5,6 & 8?
2. Find the least no. by which 294 must be multiplied to make it a perfect square?
3. Find the least number by which 1470 must be divided to get a number which is the perfect square?
4. By which least number 675 must be multiply to obtain a number which is perfect cube?
5. What is a smallest number by which 3600 divided to make a perfect cube?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Don't post so many problems in a single post. You will probably never get answers to them all. I will do one and hope that it helps you figure out how to do some or all of the others.
Here's a procedure that will help with #2 and #4 and may help with the others:- Perform prime factorization on the number.
- Pair up matching prime factors as much as possible.
- The number you are looking for is the product of all the unpaired prime factors.
Lets see how this works on #2:
1. Prime factorization.
294 = 2*147 = 2*3*49 = 2*3*7*7
2. Pair up the prime factors.
Only is only one pair of matching factors:
294 = 2*3*(7*7)
3. The number we're looking for is the product of the unpaired factors: 2*3 or 6.
Hint for #3: As it turns out, the number you divide by to get a perfect square is also the number you multiply by to get a perfect square!
Hint for #5: For perfect cubes you group three matching factors, not just two.
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