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
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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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