Question
Download Solution PDFSum of 2 natural numbers is 140 and their HCF and LCM are 28 and 168 respectively. Find the difference between the numbers.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
The sum of 2 natural numbers = 140
HCF of the numbers = 28
LCM of the numbers = 168
Concept:
If two numbers are given, one is the sum and the other is the product, then the numbers can be found using the equations: n1 + n2 = sum and n1 × n2 = product.
Solution:
⇒ Assume the numbers are a and b, where a > b. Then, a = (sum + √(sum2 - 4 product))/2 and b = (sum - √(sum2 - 4 product))/2
⇒ a = (140 + √(1402 - 428168))/2 = 84
⇒ b = (140 - √(1402 - 428168))/2 = 56
⇒ Difference = a - b = 84 - 56 = 28
Hence, the difference between the numbers is 28.
Last updated on Jul 8, 2025
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