Question

If the ratio of two numbers is 2:3 and their lcm is 54,then the sum of the two numbers are

Answer 1

Let the two numbers be 2x and 3x.
Their LCM = 54.
54/(2x)(3x) = 9/x^2.
Hence x = 3.
The numbers are 18 and 27.
The sum of the two numbers = 45.
Check: HCF*LCM = 9*54 = 486.
Product if 18*27 = 486. Correct.

Answer 2

suppose two numbers =x\y=2t\3t

then LCM would be=6t

as given,6t=54

t=9

thus numbers will be=18 and 27

so sum=45