can two numbers have 12 as their Hcf and 512 as their lcm justify your answer
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Step-by-step explanation:
If two numbers have 12 as their HCF we can represent then as
12a = 2^2 * 3 * a and 12b = 2^2 * 3 * b
Clearly both numbers would have to include 3 as a factor.
The number 512 does not contain 3 as a factor, since it is 2^9.
The sort of numbers that could both be contained by 512 can only be 512 itself and a lower power of 2 such as 64. Numbers that contain 3 as a factor cannot have 512 as their LCM, so the answer is no.
Two numbers cannot both have 12 as their HCF and 512 as their LCM
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