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Question 9
If the least common multiple of two numbers, 1728 and K is 5184, then how many values of K are possible?
Solution
Lcm 0f 1728 and K is 5184
$$1728=2^{6}*3^{3}$$
$$5184=2^{6}*3^{4}$$
So K can be $$ 2^{0}*3^{4},2^{1}*3^{4},2^{2}*3^{4},2^{3}*3^{4},2^{4}*3^{4},2^{5}*3^{4} and 2^{6}*3^{4}$$
So total of 7 values
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