Question

If two numbers are in the ratio 6 : 13 and their l.c.m. is 312, find the numbers.

Answer 1

Let the two numbers be 'x' and 'y' such that x : y = 6 : 13 ⇒ $\frac{x}{y}=\frac{6}{13}.$
We can assume that the HCF of 'x' and 'y' is a number 'k'.
So, x = 6k, and y = 13k.
Now, the product of any two numbers 'x' and 'y' is always equal to the product of their LCM and HCF
⇒ x$\times$y = 312 $\times$ k
⇒ 6k $\times$ 13k = 312 $\times$ k
⇒ k = $\frac{312}{6\times 13}=4$
⇒ k = 4
Thus, x = 6k = 6 $\times$4 = 24, and y = 13 $\times$ 4 = 52.