[email protected] wrote:
Hey Brent. I'm still a bit confused as why you chose these prime factors to multiply (2x2x2x3x3x5x7), and why you excluded others. Can you shed some light on that?
Thanks,
Tom
No problem.
Let's look at each number on its own.
To begin, we want the number, N, to be divisible by 24
24 = (2)(2)(2)(3)
So, we need three 2's and one 3 in the prime factorization of N.
In other words,
N = (2)(2)(2)(3) [so far]
We also we want N to be divisible by 36
36 = (2)(2)(3)(3)
So, we need two 2's and two 3's in the prime factorization of N.
We already have more than two 2's in the prime factorization of N, so we're good there. We also have one 3 so far, so we need to add one more
3.
So, now we have
N = (2)(2)(2)(3)(3) [so far]
We also we want N to be divisible by 42
42 = (2)(3)(7)
So, we need one 2, one 3 and one 7 in the prime factorization of N.
We already have one 2 and one 3, so we're good there. But we do need to add a
7
So, now we have
N = (2)(2)(2)(3)(3)(7)
Finally, we want N to be divisible by 60
60 = (2)(2)(3)(5)
So, we need to add a
5
So, now we have
N = (2)(2)(2)(3)(3)(7)(5)
So, when N = (2)(2)(2)(3)(3)(5)(7), N is divisible by 24, 36, 42 and 60
Since we're multiplying some number by 4 to get N, we'll take (2)(2)(2)(3)(3)(5)(7) and divide by 4 to get
630
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
