Question
The combined total of two numbers is 105. Their LCM and HCF
are 315 and 5 respectively. What is the smaller number?Solution
ATQ,
Let the smaller number = ‘x’
Greater number = (105 – x)
Product of numbers = LCM × HCF
Or, x(105 – x) = 5 × 315
Or, 105x – x² = 1575
Or, x² – 105x + 1575 = 0
Or, x² – 60x – 45x + 1575 = 0
Or, x(x – 60) – 45(x – 60) = 0
Or, (x – 60)(x – 45) = 0
So, smaller number = 45
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