Hi all. So Im feeling totally lost on the GCF/LCM/LCD type questions. I get the concept when we use real numbers, but a lof of the times i get stumped on the DS questions involving these values.

Can anyone share a quick primer on this, specific to GMAT, and share the concepts ?

greatest common FACTOR and least common MULTIPLE

Notice the words I capitalized - that should be your focus when you think about each concept. DO NOT think about "greatest" and "least" even though those are the first words; that's what messes everybody up.

Factors are smaller than or equal to the main number
eg, 1, 2, 4, and 8 are all factors of 8

Multiples are greater than or equal to the main number
eg, 8, 16, 24, and 32 are all multiples of 8

I'll show you the theoretical way of handling GCF and LCM, though if the numbers are small enough, you can also just try real numbers. But I assume you don't struggle with real numbers as much as with theory.

1) break your numbers down to their prime factors.
eg, 8 = 2*2*2 and 10 = 2*3

2) Write everything in terms of exponents:
8 = 2^3
10 = 2^1 * 5^1

3) For GCF, we want a FACTOR, so we want a SMALLER number than our starting point. Choose the smallest EXPONENT for each prime base
eg 2 is part of both 8 and 10. The smaller exponent is 1 (for 2^1, which is part of 10). Choose that.
Dealing with 5 is a little trickier because 8 doesn't have any 5's. That's the equivalent of saying 8 = 2^3 * 5^0 (remember that anything to the zero power is 1). So if you have 5^0 and 5^1, which is the smaller exponent? Zero, of course, so choose 5^0 - which means we can just ignore this because 5^0 = 1.
So, GCF = 2

4) For LCM, we want a MULTIPLE, so we want a LARGER number than our starting point. Choose the largest EXPONENTS.
eg for 2, the largest exponent is 3, so select 2^3. For 5, the largest exponent is 1, so select 5^1. Multiply these to get 2^3 * 5^1 = 8*5 = 40.

Try with some harder numbers. Find the LCM and GCF of 18 and 60. (Try this before you look at the solution below!!)
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18 = 2*3*3 = 2^1 * 3^2
60 = 2*2*3*5 = 2^2 * 3^1 * 5^1

18 doesn't contain any 5's, so I'm going to rewrite it as: 2^1 * 3^2 * 5^0

GCF - choose smaller exponents
2^1
3^1
5^0
multiply to get 6

LCM - choose larger exponents
2^2
3^2
5^1
multiply to get 180

Awesome Stacy! That really helped!

Mike

thank you very much

There is some mistakes in your post stacey...
- LCM of 18 & 60 is 180 and GCF is 6
- GCF of 8 & 10 is 2
I'm sure they were just typos but future gmat students may get a little confused

GCF and LCM are definitely confusing! Thanks for the heads up on the typos... I took the liberty of editing Stacey's (otherwise very clear) post.

Rey

Stacey, Im absolutely indebted to you for your clear and concise post. In fact, kudos to the entire MGMAT staff that helps out here. Top notch work !!

Whoops! Thanks for the catch on the typos, guys!