Three number are in the ratio of 2: 3 : 5 and their L.C.M. is 2400. Their H.C.F. is:Options :20406080

The three numbers are in the ratio 2:3:5. Let's assume the numbers are 2x, 3x, and 5x.

The LCM of these numbers is given as 2400.

The LCM of numbers in ratio form is calculated as the product of the ratio and the HCF.

So, 2x3x5x = 2400

From this, we can calculate the value of x.

x = cube root of (2400/30) = 4

The HCF is the product of the common ratio (x) and the HCF of the numbers in the ratio.

Since the numbers in the ratio are co-prime (2,3,5), their HCF is 1.

So, the HCF of the numbers is x1 = 41 = 4

Therefore, the HCF of the numbers is 4.