Question

22. The LCM of two consecutive even numbers is 144, find the numbers? (1) 16 and 18 (2) 14 and 16 (3) 18 and 20 (4) 22 and 24

11th - 12th Class

Maths

Solution

471

4.0 (1 ratings)

22. (1) Two consecutive even numbers be ( x ) and ( x+2 ) Given, ( L C M=144 ) ( because ) We can logically say that the ( mathrm{HCF} ) of any two consecutive even numbers is always equal to '2' provided that the smallest no, is at least '2'. ( because H C F=2 ) According to the question, [ x times(x+2)=2 times 144 ] ( Rightarrow quad x^{2}+2 x-288=0 ) ( Rightarrow quad x^{2}+18 x-16 x-288=0 ) ( Rightarrow quad x(x+18)-16(x+18)=0 ) ( Rightarrow quad(x+18)(x-16)=0 ) ( therefore ) ( x=16 ) Hence, the numbers are 16 and 18 .