M28-33

Hi HisHo,

Because if x = 1, then the lcm of 1, 4^3 and 6^5 will not be 6^6.

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Hi,

It took me a lot of time to understand this answer explanation but after I re-read my notes about LCM I was able to understand it to the full.

To all others who are still struggling, the rule of LCM is "When you combine two factor trees (prime factors) of two numbers to arrive at an LCM that contain overlapping primes, you drop the overlap".

In this case, it is given that 6^6 = 2^6 x 3^6 is the LCM of

X as "A"

4^3 = 2^6 as "B"

6^5 = 2^5 and 3^5 as "C"

Now, the LCM will have 2^6 from B, dropping out 2^5 from C, 3^6 from A (thinking we start with 3^6), dropping out 3^5 from C.

Now, as we ware asked to give all the possible values of X, we can write down that it can have

3^6
2 x 3^6
2^2 x 3^6
2^3 x 3^6
2^4 x 3^6
2^5 x 3^6
2^6 x 3^6

as all the values with 2 power will be dropped for overlapping with other numbers. Note that 2^7 x 3^6 will be wrong as it will increase the number of 2s adding one more to the LCM which is not what was given in the question.

This is my first ever explanation to an answer on GC. Hope you found it helpful. If not sorry for the confusion.

Thank you!!

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

I think this is a high-quality question and I agree with explanation.

Dears ScottTargetTestPrep VeritasKarishma
Why we couldn't take 1 as a value for X?

I think this is a high-quality question and I agree with explanation.