Question

The L.C.M. of two consecutive even numbers is 264. Find the sum of those two
numbers.
a) 42
b) 46
c) 56
d) 48

​

Answer 1

THE ANSWER IS 42

THE ANSWER IS 42

Answer 2

Answer:

Let the two consecutive even numbers be 2x and 2x + 2.

so its LCM is 2x(x + 1)

According to statement

$2x(x + 1) = 264 \\ x(x + 1) = 132 \\ {x}^{2} + x - 132 = 0 \\ {x}^{2} + 12x - 11x - 132 = 0 \\ x(x + 12) - 11(x + 12) = 0 \\ (x + 12)(x - 11) = 0 \\ x = 11$

Hence numbers are 22, 24.

So sum = 22 + 24 = 46