What is the other number when the LCM of two numbers is 14 times their HCF, and their sum is 600?

To find the other number when one number is given as 280, we can use the relationship between the LCM (Least Common Multiple) and the HCF (Highest Common Factor).

Given the following information:

• LCM = 14 × HCF
• LCM + HCF = 600
• One number (let’s call it A) = 280
• Let the other number be B.

First, we can express the LCM and HCF in terms of HCF:

• Let HCF = x
• Then, LCM = 14x

According to the second piece of information, we have:

14x + x = 600

Simplifying this gives:

15x = 600

Now, solving for x:

x = 600 / 15 = 40

Thus, the HCF is 40 and the LCM will be:

LCM = 14 * 40 = 560

Now we use the relation between two numbers, their LCM, and HCF:

LCM = (A * B) / HCF

Substituting the known values:

560 = (280 * B) / 40

Cross-multiplying to solve for B gives:

560 * 40 = 280 * B

This simplifies to:

22400 = 280 * B

Now dividing both sides by 280:

B = 22400 / 280 = 80

Therefore, the other number is 80.