Question : $A=2^K×3^5$ and $B=2^5×3^7$. If the least common multiple of A and B is $2^8×3^7$, then what is the value of K?
Option 1: 6
Option 2: 8
Option 3: 9
Option 4: 3
Correct Answer: 8
Solution :
Given: $A=2^K×3^5$ and $B=2^5×3^7$
⇒ $A = 2^k × 3^5$ and $B = 2^5 × 3^7$
We have to take the highest power of the number from the above value
The highest power of 3 = 7
Given: LCM of A and B = $2^8 × 3^7$
The highest power of 2 is 8
The power of 2 is $k$ and 8
From A and B, the highest power of 2 is 8
Hence, the correct answer is 8.
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