Question
Download Solution PDFThree number are in the ratio of 4 ∶ 5 ∶ 6, and their LCM is 180. Their HCF is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Ratios of numbers: 4 : 5 : 6
LCM of the numbers: 180
Concept:
When three numbers are in the ratio a:b:c, and their LCM is n, then their HCF is n/(abc).
Solution:
HCF of the numbers = 180/LCM of (4, 5 and 6) = 180/60 ⇒ 3
Therefore, their HCF is 3.
Alternate Method
Ratio of numbers = 4 : 5 : 6
Let numbers be 4x, 5x and 6x where x is the HCF of numbers.
So
LCM of (4x, 5x, 6x) = 60x
60x = 180
so
x = 3 = HCF of numbers
So 3 is the correct answer.
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