Question

The ratio of two natural numbers is 4:5 and their lcm is 360

Answer 1

$\textsf{I think your question should be:}$

$\textsf{The ratio of two natural numbers is 4:5}$

$\textsf{and their lcm is 360. Find the numbers}$

$\textsf{Let the two numbers be a and b}$

$\textsf{Given:}$

$\mathsf{a:b=4:5}$

$\textsf{Then,}$

$\mathsf{a=4k\;\;\&\;\;b=5k}$

$\implies\mathsf{a=2^2{\times}k\;\;\&\;\;b=5{\times}k}$

$\textsf{L.C.M}\mathsf{=2^2{\times}k{\times}5=20k}$

$\textsf{L.C.M=360}$

$\implies\mathsf{20k=360}$

$\implies\mathsf{k=\frac{360}{20}}$

$\implies\mathsf{k=18}$

$\mathsf{a=4(18)=72}$

$\mathsf{b=5(18)=90}$

$\therefore\textsf{The required numbers are 72 and 90}$

Answer 2

The ratio of the two natural numbers is 4:5 and their LCM is 360 . We know that the product of the two numbers will be equal to the product of their LCM and HCF. We suppose that the numbers are 4x and 5x. LCM is equal to 20x for these numbers. Thus,  we obtain 20x= 360 . Thus, x=18 .The numbers will will be 4*18=72 and 5*18=90. Thus, the numbers will be 72 and 90 .