Question
The sum of two numbers is 144. Their LCM is 540 and HCF is
15. What is the smaller number?Solution
ATQ,
Let the smaller number = ‘x’
Greater number = (144 – x)
Product of the numbers = LCM × HCF
Or, x(144 – x) = 15 × 540
Or, 144x – x² = 8100
Or, x² – 144x + 8100 = 0
Or, x² – 90x – 54x + 8100 = 0
Or, x(x – 90) – 54(x – 90) = 0
Or, (x – 90)(x – 54) = 0
So, smaller number = 54
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