The 19-year cycle (called the Metonic cycle) does not equal exactly 223 months — it equals 235 synodic months (lunar months, from one new moon to the next).
The number 223 synodic months is actually for a different cycle: the Saros cycle, which is about 18 years and 11 days long. The Saros is used mainly for predicting eclipses (both solar and lunar) because it brings the Sun,
Moon, and Earth's nodes back into very similar alignment, so similar eclipses repeat after one Saros.
Quick comparison
• Metonic cycle → 19 tropical years ≈ 235 synodic months
• This is the one used in the Hebrew (Jewish) calendar ("God's Lunisolar Calendar") to keep months tied to the moon while aligning holidays with the seasons over the long term.
• 19 years have 12 × 12 = 228 months normally, plus 7 extra (leap) months = 235 total months.
• The match is very close but not perfect (off by about 2 hours per 19 years), so the calendar drifts very slowly.
• Saros cycle → 223 synodic months by definition ≈ 18 years + 11 days + 8 hours
• This repeats eclipse patterns (same type, roughly same duration and path).
• It's shorter and doesn't aim to sync with the seasons or calendar years the way the Metonic does.