Question
Two numbers add up to 98. If the LCM of the numbers is 315
and the HCF is 9, find the smaller of the two numbers.Solution
ATQ,
Let the smaller number = ‘x’
Greater number = (98 – x)
Product of the numbers = product of their LCM and HCF
Or, x(98 – x) = 9 × 315
Or, 98x – x² = 2835
Or, x² – 98x + 2835 = 0
Or, x² – 63x – 35x + 2835 = 0
Or, x(x – 63) – 45(x – 63) = 0
Or, (x – 63)(x – 45) = 0
Or, x = 63, 45
So, smaller number = 45
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