Question:
If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then a =
(a) 2
(b) 3
(c) 4
(d) 1
Solution:
$\operatorname{LCM}(a, 18)=36$
$\operatorname{HCF}(a, 18)=2$
We know that the product of numbers is equal to the product of their HCF and LCM.
Therefore,
$18 a=2(36)$
$a=\frac{2(36)}{18}$
$a=4$
Hence the correct choice is (c).