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Question 74
The HCF and LCM of 2 numbers are 2 and 60 respectively. If one of the numbers is 14 more than the other, then the smaller number is:
Solution
Let one number be x
Then other number will be x+14
We know that Product of two numbers = Product of LCM and HCF
$$x \times (x+14) = 2 \times 60$$
=> $$x^2 + 14x = 120$$
=> $$x^2 + 14x - 120 = 0$$
=> $$x^2 + 20x - 6x - 120 = 0$$
=> x(x+20) - 6(x+20) = 0
=> (x-6)(x+20) = 0
x = 6 or -20
Here, One number is 6, then the other number is 6+14 = 20
Therefore, The smallest number is 6.
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