Question
The total of two numbers is 130. If their LCM is 432 and
HCF is 12, determine the smaller number.Solution
ATQ,
Let the smaller number = ‘x’
Greater number = (130 – x)
Product of the numbers = product of their LCM and HCF
Or, x(130 – x) = 12 × 432
Or, 130x – x² = 5184
Or, x² – 130x + 5184 = 0
Or, x² – 72x – 58x + 5184 = 0
Or, x(x – 72) – 58(x – 72) = 0
Or, (x – 72)(x – 58) = 0
Or, x = 72, 58
When x = 72, (130 – x) = 58
Therefore, x = 58
So, the smaller number = 58
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