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Question
Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
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Solution
Let the first number be 2x and the second be 3x
∴ Their LCM = 2 × 3 × x
But given LCM = 180
∴ 2 × 3 × x = 180
`\implies` x = 30
First number = 2x = 2 × 30 = 60 = 2 × 2 × 3 × 5
Second number = 3x = 3 × 30 = 90 = 3 × 3 × 2 × 5
Now, HCF of 60 and 90 = 2 × 3 × 5 = 30
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