SOLUTION: LCM of {{{12^24}}},{{{16^18}}} and {{{N}}} is {{{24^24}}} then number of possible value of {{{N}}}

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: LCM of {{{12^24}}},{{{16^18}}} and {{{N}}} is {{{24^24}}} then number of possible value of {{{N}}}       Log On


   

Question 1172862: LCM of 12%5E24,16%5E18 and N is 24%5E24 then number of possible value of N
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The two given numbers are

12%5E24+=+%28%282%5E2%29%283%5E1%29%29%5E24+=+%282%5E48%29%283%5E24%29

16%5E18+=+%282%5E4%29%5E18+=+2%5E72

The LCM is

24%5E24+=+%28%282%5E3%29%283%5E1%29%29%5E24+=+%282%5E72%29%283%5E24%29

So the given LCM is the LCM of just the two given numbers.

That means the third number N can be any number of the form

%28%282%5Ea%29%283%5Eb%29%29

in which

0%3C=a%3C=72 (73 choices)

and

0%3C=b%3C=24 (25 choices)

ANSWER: The number of possible values of N is 73*25 = 1825.