Answer:
The two numbers are 12 and 26
Step-by-step explanation:
let the first number = a
let the second number = b
The ratio of the numbers is given as;
[tex]\frac{a}{b} = \frac{6}{13} \\\\a = \frac{6b}{13}[/tex] -------- (1)
The lcm of the two numbers is given as;
a x b = 312
ab = 312 --------- (2)
From equation (1), [tex]a = \frac{6b}{13}[/tex]
[tex]b(\frac{6b}{13} ) = 312\\\\\frac{6b^2}{13} = 312\\\\6b^2 = 4056\\\\b^2 = \frac{4056}{6} \\\\b^2 = 676\\\\b = \sqrt{676} \\\\b = 26\\\\From \ equation \ (1);\\\\a = \frac{6b}{13} \\\\a = \frac{6 \times 26}{13} \\\\a = 12[/tex]
Therefore, the two numbers are 12 and 26
