Need help with a math problem!

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1

<p>Hey guys!</p>

<p>Anyways if you guys could please help me with this math problem, IDK if it's the way I'm reading it but I'm getting very confused and ending with different answer. Also this is a question from PWN the SAT.</p>

<p>So anyways, </p>

<p>If P^2 is a multiple of both 8 and 35, and p is an integer, what is the least possible value of p?</p>

<p>So the way I did it is that
Let X-number of times the number has been multiplied
Let Y-number of times the number has been multiplied
8X=P^2
37Y=P^2</p>

<p>Any thoughts?</p>

2

<p>Don’t you mean 35Y?</p>

3

<p>I think it’s 4900… not sure, though</p>

4

<p>The answer is 140</p>

5

<p>An easy way to do it: P^2 is divisible by the LCM of 8 and 35 (which is 280). 280 = (2^3)<em>5</em>7. Therefore P must be divisible by 5 and 7, and P must contain at least two 2’s in it (if P had one 2, then 4 would completely divide P, we don’t want that). So the minimum value of P is (2^2)<em>5</em>7 = 140.</p>