UPSC 2013 CDS 2 Math Paper

HCF (a, b) = 1 ⇒ a and b have no common factor other than 1.
HCF (a,c) = 1
⇒a and c have no common factor other than 1.
So, a and bc have no common factor other than 1.
⇒HCF of (a, bc) = 1
Trick:
Take a = 2, b = 3, c = 5. Then
HCF(2, 3) = 1
HCF(2, 5) = 1
∴ HCF(2, 3×5) = HCF(2, 15) = 1