SOLUTION: 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 w

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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