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The G.C.D of two numbers is 23. The other two factors of the L.C.M are 13 and 14. What is the larger number?
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Not sure what to do about this one. I got it till how the L.C.M is divisible by 23, 13 and 14... but may I assume that the L.C.M IS $23 \cdot 13 \cdot 14$? If so, why?

Question

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The G.C.D of two numbers is 23. The other two factors of the L.C.M are 13 and 14. What is the larger number?
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Not sure what to do about this one. I got it till how the L.C.M is divisible by 23, 13 and 14... but may I assume that the L.C.M IS $23 \cdot 13 \cdot 14$? If so, why?

parthkohli · Answer

Is it funny that I'm not getting the answer to this question on both M.SE and OpenStudy?

hartnn · Answer

the 2 numbers which satisfy both the conditions are 23*13 and 23*14 ....

parthkohli · Answer

Oh yes!

parthkohli · Answer

Wait, let me have another look at the question. That was a nice solution.

parthkohli · Answer

Okay, so $23 \cdot 14 = 322$.

hartnn · Answer

yup, thats the larger no.

hartnn · Answer

i liked the M.SE solution too....much detailed.

parthkohli · Answer

Wait, is there a logical explanation for that according to logic or was it just another trick?

parthkohli · Answer

Oh, I didn't see it right there...haha

parthkohli · Answer

I do not understand that solution too well. I like to be explained in a simple language with hints. :|