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Number Systems-LCM & HCF -MGMAT

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by theCodeToGMAT » Mon Oct 14, 2013 1:31 am
Please post answer choices as well.
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by Uva@90 » Mon Oct 14, 2013 1:32 am
sukhman wrote:If the LCM of a and 12 is 36 , what are the possible values of a ?
a can be 9...
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by sukhman » Mon Oct 14, 2013 1:51 am
It simply says 9 , 18 and 36 could be possible values of a
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by theCodeToGMAT » Mon Oct 14, 2013 2:03 am
LCM of a & 12 = 36 = 2 x 2 x 3 x 3
You need to arrange 2^2 and 3^3 so that LCM is always 36. We need to give at least 3^2 to "a" so that 3^2 appears in LCM. So,

a = 3 x 3 x _ --> (9, is possible)
12 = 2 x 2 x 3

Also, we can give one & two "2" to "a" without impacting the 2^2 in 36
So,

a = 3 x 3 x 2 --> (18, is possible)

and

a = 3 x 3 x 2 x 2 --> (36, is possible)
12 = 2 x 2 x 3
Notice that if we try to further put "2" or "3" then the LCM "36" will be impacted.
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by lunarpower » Mon Oct 14, 2013 3:09 am
If you hit a wall with the prime-number treatment, you can also just make a list.
The LCM of a and 12 is 36. So, a is definitely a factor of 36.
Try all the factors of 36, and see which ones actually work. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
* The LCM of 1 and 12 is 12, not 36.
* The LCM of 2 and 12 is 12, not 36.
* The LCM of 3 and 12 is 12, not 36.
* The LCM of 4 and 12 is 12, not 36.
* The LCM of 6 and 12 is 12, not 36.
* The LCM of 9 and 12 is 36. a = 9 is an acceptable value.
* The LCM of 12 and 12 is 12, not 36.
* The LCM of 18 and 12 is 36. a = 18 is an acceptable value.
* The LCM of 36 and 12 is 36. a = 36 is an acceptable value.

So, 9, 18, and 36.
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