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Question 68
$$A = 2^{K} \times 3^{5}$$ and $$B = 2^{5} \times 3^{7}$$. If the least common multiple of A and B is $$2^{8} \times 3^{7}$$ , then what is the value of K?
Solution
$$A = 2^{K} \times 3^{5}$$Â Â Eq.(i)
$$B = 2^{5} \times 3^{7}$$ Eq.(ii)
If the least common multiple of A and B is $$2^{8} \times 3^{7}$$ Eq.(iii)
From Eq.(i), Eq.(ii) and Eq.(iii), we can say that LCM(least common multiple) in terms of the power of 3 is 7. Similarly, we can say that LCM(least common multiple) in terms of the power of 2 is 8 by comparing them.
So the value of K = 8
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