22. The LCM of two consecutive even...
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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
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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 .
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