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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