alleryIf $\text{HCF}(a, b) = 12$ and $\text{LCM}(a, b) = 180$, then the number of possible ordered pairs $(a, b)$ is
A2
B6
C1
D4
Answer & Solution
Correct answer: D. 4
Write $a = 12m$, $b = 12n$ with $\gcd(m,n)=1$ and $mn = 180/12 = 15$.
**Coprime factor pairs of 15:** $(1,15),(15,1),(3,5),(5,3)$ — 4 ordered pairs.
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