turkey-yks 2025 Q4

turkey-yks · Other · yks-ayt Number Theory GCD, LCM, and Coprimality
Let $a, b, c$ and $d$ be positive integers. $$\begin{aligned} & M = 6^{a} \cdot 5^{b} \\ & N = 10^{c} \cdot 9^{d} \end{aligned}$$ For the numbers $M$ and $N$ $$\begin{aligned} & \gcd(M, N) = 2^{3} \cdot 3^{2} \cdot 5 \\ & \text{lcm}(M, N) = 2^{5} \cdot 3^{3} \cdot 5^{5} \end{aligned}$$ are given. Accordingly, what is the sum $a + b + c + d$?
A) 8 B) 9 C) 10 D) 11 E) 12
Let $a, b, c$ and $d$ be positive integers.
$$\begin{aligned}
& M = 6^{a} \cdot 5^{b} \\
& N = 10^{c} \cdot 9^{d}
\end{aligned}$$
For the numbers $M$ and $N$
$$\begin{aligned}
& \gcd(M, N) = 2^{3} \cdot 3^{2} \cdot 5 \\
& \text{lcm}(M, N) = 2^{5} \cdot 3^{3} \cdot 5^{5}
\end{aligned}$$
are given.
Accordingly, what is the sum $a + b + c + d$?

A) 8
B) 9
C) 10
D) 11
E) 12