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No. For example, a 12x1 and a 4x3 quadrilateral both have an area of 12, but they are not congruent.
12x1=12 12x2=24 12x3=36 12x4=48 12x5=60 12x6=72
12x1=12 12x2-24 12x3=36 12x4=48 12x5=60 12x6=72 12x7=84 12x8=96 12x9=108 12x10-120 12x11=132
The LCM is 36. In this case it is easy to look at the multiples of 12. The first one is 12x1 and that does not work. 24 is 12x2 and 9 does not go into that. But 36 is 12x3 and both 6 and 9 divide it evenly. So that tells us the LCM is 36.
364 1x12=12 2x11=22 3x10=30 4x9=36 5x8=40 6x7=42 7x6=42 8x5=40 9x4=36 10x3=30 11x2=22 12x1=12 Added up equals 364