Question : If A = 23 × 37, B = 27 × 35 and C = 28 × 34, then what is the least common multiple of A, B and C?
Option 1: 27× 37
Option 2: 26 × 37
Option 3: 28 × 37
Option 4: 29 × 37
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Correct Answer: 2 8 × 3 7
Solution : LCM is the product of Prime factors with the highest power Here, the Prime factors are: A = $2^3 \times 3^7$ B = $2^7 \times 3^5$ C = $2^8 \times 3^4$ The highest power for 2 is 2$^8$ The highest power for 3 is 3$^7$ $\therefore$ LCM = $2^8 \times 3^7$ Hence, the correct answer is 2 8 × 3 7 .
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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?
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