Question

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 .

# 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

Solution