Question

HCF(320, x) = 20, LCM(320, x) = 2240, then x =

Answer 1

140

Explanation:

When working HCF and LCM problems, I like to think in terms of this little diagram:

(a [ b ) c]

It shows me one of the numbers is ab, the other is bc, the HCF is b and the LCM is abc. "a" and "c" must be relatively prime for "b" to be the HCF.

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Here, we're given ...

b = 20

ab = 320

abc = 2240

Then ...

c = abc/(ab) = 2240/320 = 7

x = bc = 20(7) . . . . . . equivalently, x = (abc·b)/(ab) = (2240·20)/320

x = 140