Question

# The LCM of two numbers is 567 and their HCF is 9. If the difference between the two numbers is 18, find the two numbers.(A) 36 and 18(B) 78 and 60(C) 63 and 81(D) 52 and 34

Product of two number = LCM$\times$HCF= 567×9 = 5103
$\Rightarrow {x^2} + 19x - 5103 = 0 \\ \Rightarrow {x^2} + 81x - 63x - 5103 = 0 \\ \Rightarrow x\left( {x + 81} \right) - 63(x + 81) = 0 \\ \Rightarrow \left( {x - 63} \right)\left( {x + 81} \right) = 0 \\$