document.write( "Question 1172862: LCM of $\"12%5E24\"$ , $\"16%5E18\"$ and $\"N\"$ is $\"24%5E24\"$ then number of possible value of $\"N\"$ \n" ); document.write( "

Algebra.Com's Answer #798018 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The two given numbers are

\n" ); document.write( " $\"12%5E24+=+%28%282%5E2%29%283%5E1%29%29%5E24+=+%282%5E48%29%283%5E24%29\"$

\n" ); document.write( " $\"16%5E18+=+%282%5E4%29%5E18+=+2%5E72\"$

\n" ); document.write( "The LCM is

\n" ); document.write( " $\"24%5E24+=+%28%282%5E3%29%283%5E1%29%29%5E24+=+%282%5E72%29%283%5E24%29\"$

\n" ); document.write( "So the given LCM is the LCM of just the two given numbers.

\n" ); document.write( "That means the third number N can be any number of the form

\n" ); document.write( " $\"%28%282%5Ea%29%283%5Eb%29%29\"$

\n" ); document.write( "in which

\n" ); document.write( " $\"0%3C=a%3C=72\"$ (73 choices)

\n" ); document.write( "and

\n" ); document.write( " $\"0%3C=b%3C=24\"$ (25 choices)

\n" ); document.write( "ANSWER: The number of possible values of N is 73*25 = 1825.

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