# Number of values of $k$ such that $LCM(6^6,8^8,k)=(12)^{12}$

The question is to find out the number of values of $k$ such that $$LCM(6^6,8^8,k)=(12)^{12}$$

I tried using the formula $$abc=\frac{LCM(6^6,8^8,k) HCF(6^6,k) HCF(8^8,k)HCF(k,6^6)}{HCF(6^6,8^8,k)}$$ but couldn't figure out anything from this.Any help shall be highly appreciated. Thanks.

Let $k=2^{a} 3^b$
Since LCM of $2^63^6 ~(6^6)$ and $2^{24} ~(8^8)$ and $2^{a} 3^b (k)$ is $2^{24}3^{12} ~(12^{12})$
LCM of $6,24$ and $a$ should be $24$ and LCM of $6$ and $b$ should be $12$.