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Question 45
The LCM of two numbers x and yis 204 times their HCF. If their HCF is 12 and the difference between the numbers is 60, then x + y = ?
Solution
HCF = 12
LCM = 204 $$\times$$ 12
xy =Â 204 $$\times$$ 12Â $$\times$$ 12 = 29376
x - y = 60
$$(x - y)^2$$ = 3600
$$x^2 + y^2 -2xy = 3600$$
$$x^2 + y^2 -2xy = 3600$$
$$(x + y)^2 -4xy = 3600$$
$$(x + y)^2 = 3600 + 4 \times 29376$$
$$(x + y)^2 = 121104$$
x + y = 348
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