If the least common multiple (LCM) of two numbers is 14 times their highest common factor (HCF) and the sum of the LCM and HCF is 600, with one number being 280, how do we find the other number?

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Finding the Other Number

Given that:

  • LCM = 14 * HCF
  • LCM + HCF = 600
  • One number = 280

Let
HCF = x.
Therefore, the LCM can be expressed as:

LCM = 14x

From the information provided, we can form the equation:

14x + x = 600

Simplifying this gives:

15x = 600

Solving for x:

x = 600 / 15 = 40

We now know:

  • HCF = 40
  • LCM = 14 * 40 = 560

Next, let’s find the other number. The relationship between two numbers (let’s call them A and B) in relation to their LCM and HCF can be expressed as:

A * B = LCM * HCF

Substituting the known values:

280 * B = 560 * 40

Calculating the right-hand side:

280 * B = 22400

Now, divide both sides by 280:

B = 22400 / 280

Calculating B gives:

B = 80

Thus, the other number is 80.

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