Question

which two consecutive even numbers have an LCM of 180?​

Answer 1

$Two \: consecutive \: even \: terms \: and \: LCM = 180 \\ let's \: use \: two \: terms \\ = 1) \: 2x \\ = 2) \: 2x + 2 \\ \\ a \times b = HCF \times LCM \\ = HCF \: of \: 2x \: and \: 2x + 2 \\ Therefore, \\ 2x \times (2x + 2) = hcf \times lcm \\ 2x \times (2x + 2) = 2 \times 180 \\ x \times (2x + 2) = 180 \\ {2x}^{2} + 2x - 180 = 0 \\ \\ x = 9, \: - 10 \\ Therefore, \\ = 2 \times 9 = 18 \\ = 2 \times 9 + 2 = 18 + 2 = 20$

Therefore, the two consecutive even numbers are 18 and 20.