Question

LCM of ${12}^{24},{16}^{18},$ and N is ${24}^{24}$. The number of all the possible values of N = S. What is the value of S?

• A. 25
• B. 1800
• C. 1825
• D. None of these

Answer 1

The correct option is C 1825

It is given that LCM of ${12}^{24},{16}^{18}$ and $N={24}^{24}Or,3^{24}\times 2^{48},2^{72}$ and $N=2^{72}\times 3^{24}$
From here, the value of N can be $2^{0-72}\times 3^{0-24}$
Then, total number of value = $(72+1)(24+1)=1825$