Question
Download Solution PDFIf the ratio of two numbers is in the ratio 4 ∶ 9 and their LCM is 720, then find the sum of both the numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Ratio of numbers = 4 ∶ 9
LCM of the numbers = 720
Calculation:
Let the numbers be 4a and 9a.
∴ Prime factors of 4a = a × 2 × 2
Prime factors of 9a = a × 3 × 3
∴ LCM of 4a and 9a = a × 2 × 2 × 3 × 3
= 36 × a
∵ LCM of 4a and 9a = 720 ------(Given)
∴ 36 × a = 720
⇒ a = 720/36
⇒ a = 20
∴ Numbers are 4a = 4 × 20 = 80
9a = 9 × 20 = 180
∴ Sum of numbers = 180 + 80
= 260
Last updated on May 1, 2025
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