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other 2 are odd= (2x+1) and (2x-1)

so, (2x+1) + 2x + (2x-1)=48

2x+2x+2x=48

6x=48

x=8.

so the three numbers are= 15,16,17.

i.e. 3x+3=48

or,3x=48-3=45

So, the three consequtive numbers are 15,16,17 out of which only 16 is even.