Question
Two numbers have a sum of 112. If their LCM is 420 and HCF
is 6, determine the smaller number.Solution
ATQ,
Let the smaller number = ‘x’
Greater number = (112 – x)
Product of numbers = LCM × HCF
Or, x(112 – x) = 6 × 420
Or, 112x – x² = 2520
Or, x² – 112x + 2520 = 0
Or, x² – 84x – 28x + 2520 = 0
Or, x(x – 84) – 28(x – 84) = 0
Or, (x – 84)(x – 28) = 0
So, smaller number = 28
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