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# The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, find the other number

The smallest positive number that is a multiple of two or more numbers is known as the LCM or least common multiple

## Answer: If the LCM of two numbers is 14 times their HCF and the sum of LCM and HCF is 600, one number being 280, the other number is 80

The greatest number which divides each of the two or more numbers is called HCF or Highest Common Factor

**Explanation:**

Given: The first number is 280

Let the other number be ′x′

According to the question,

LCM = 14HCF ---------------------------------- (1)

LCM + HCF = 600 ------------------------------ (2)

Now, substituting equation(1) in equation(2)

⇒14HCF + HCF = 600

⇒15HCF = 600

⇒HCF = 40

Thus, LCM = 14×40 = 560 (from equation(1))

Since,

HCF × LCM = Product of the two numbers

=> 40 × 560 = 280 × x (Since the first number is 280 and the second number is assumed to be x)

⇒x = 28040×560

⇒x = 40×2

⇒x = 80

Thus, the other number is 80

### Therefore, if the LCM of two numbers is 14 times their HCF and the sum of LCM and HCF is 600, one number being 280, the other number is 80

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