Question
Download Solution PDFThree numbers are in the ratio of 2 ∶ 3 ∶ 5 and their LCM is 90. Find their HCF.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The numbers are in the ratio of 2 : 3 : 5
LCM of the numbers = 90
Calculation:
Let the number be 2x, 3x and 5x.
LCM of (2x, 3x and 5x) = 2 × 3 × 5 × (x)
⇒ 30x
According to the question, 30x = 90
⇒ x = 90/30
⇒ x = 3
So, the numbers are 6, 9, 15
Now,
6 = 2 × 3
9 = 32
15 = 3 × 5
So, HCF = 3
∴ The H.C.F. of the three numbers is 3.
Last updated on Jul 8, 2025
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