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Secondary 1 | Maths
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Hania
Hania

Secondary 1 chevron_right Maths chevron_right Singapore

Please help ASAP! :)

Date Posted: 5 years ago
Views: 243

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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
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For perfect squares, the powers of each prime number must be a multiple of 2 (so that the prime numbers can be split equally into two brackets).

For perfect cubes, the powers of each prime number must be a multiple of 3 (so that the prime numbers can be split equally into three brackets).

For numbers which are both perfect squares and perfect cubes, the powers of each prime number must be a multiple of 2 AND 3 i.e. a multiple of 6 (so that the prime numbers can be split equally into six different brackets).

360 = 2^3 x 3^2 x 5.

We need each power of the prime number to be a multiple of 6, minimally 6.

To do so, we need three more '2's, four more '3's and five more '5's. This must come from the k.

So k is the product of the three '2's, four '3's and five '5's, totalling 2025000.