Question

The lcm of three distinct numbers a, b and c is 288 and their hcf is 24. If a = 24 and b, c are consecutive multiples of their hcf, then what is the greatest value that c can take?

Answer 1

Answer:

the answer is 2008456443+99854894479

Answer 2

The greatest value of c can be 96.

Step-by-step explanation:

Given,

HCF of three numbers = 24

a = 24

LCM of three numbers = 288

Let the three numbers a,b,c are a = 24x,b= 24y, c=24z

Since a =24

⇒So a= 24,b= 24y,c= 24z

Now,LCM of (a,b,c) = 24yz

        ⇒ 288 = 24yz

        ⇒yz =$\frac{288}{24}$

       ⇒yz = 12

Here, yz = 4 × 3 = 3 × 4

⇒Either y = 4,z=3 or y=3,z=4

So b = 24×3 or 24×4

        = 72 or 96

Similarly c = 24×3 or 24×4

                 = 72 or 96

Hence,the greatest value of c can be 96.