Question

The L.C.M. of two numbers is $84$ times their H.C.F. If one of the numbers is $360$ and the sum of H.C.F. and L.C.M. is $2550$, then the other number is

• A. $210$
• B. $260$
• C. $270$
• D. $190$

Answer 1

The correct option is A $210$

$LCM=84s,HCF=s$

$LCM+HCF=2550$

$84s+s=2550$

$85s=2550$

$s=\frac{2550}{85}=30$

$LCM\times HCF=$ Product of numbers

$84s\times s=360\times p$

$84\times 30\times 30=360\times p$

$p=\frac{75600}{360}=210$,

Therefore, $,$ $A$ is the correct answer.