The highest common factor (HCF) of two numbers is 18. The lowest common multiple (LCM) of the two numbers is 216. Written as a product of its prime factors, \(216=2^3\times3^3\). Both numbers are greater than 25. Find the two numbers.[2]
Written as a product of its prime factors, \(11664=2^4\times3^6\).
Explain why 11664 is a perfect square.[1]
The number \(11664\div\dfrac6m\) is a perfect cube, where \(m\) is a prime number. Find the value of \(m\).[1]
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Answer:(a) \(54,72\) (b)(i) even indices (ii) \(m=3\)