Question

If two numbers are in the ratio 6:13 and their LCM is 312, then find the numbers.​

Answer 1

The two numbers are 12 and 26

Explanation:

let the first number = a

let the second number = b

The ratio of the numbers is given as;

`(a)/(b) = (6)/(13) \\\\a = (6b)/(13)` -------- (1)

The lcm of the two numbers is given as;

a x b = 312

ab = 312 --------- (2)

From equation (1),
`a = (6b)/(13)`

`b((6b)/(13) ) = 312\\\\(6b^2)/(13) = 312\\\\6b^2 = 4056\\\\b^2 = (4056)/(6) \\\\b^2 = 676\\\\b = √(676) \\\\b = 26\\\\From \ equation \ (1);\\\\a = (6b)/(13) \\\\a = (6 * 26)/(13) \\\\a = 12`

Therefore, the two numbers are 12 and 26