There was a pattern on model numbers from the early 1960 to the late 1970s. (The model number syntax changed at that time to prevent repetition, although the letters were similiarly-used.)
The 2nd character designates the year. L in first position is laundry product. A in 3rd position is automatic washer. E is electric dryer. I is gas dryer. I'm not positive on *exactly* how the years break down. Not all letters of the alphabet were used in sequence. Some were reserved for product line and color.
LJA = 1962 (possibly 1961, our LJA washer was purchased in January 1962)
LMA = 1964
LXA = 1972
LAA = 1973-74
LDA = 1975-76
LFA = 1976-77
LHA = 1978/79
K, P, R, S, T, V were used for years, I think. Q may have been. Fill in the gaps above accordingly.
Serial numbers can tell the year and week-of-the-year of manufacture, but I'm not sure how to interpret it.
Perhaps Leslie/MagicClean can clarify?