Question

Can two numbers have 12 as their HCF and 512as their LCM ? Justify your answer.​

Answer 1

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