Nic,
Matt's posting reminded me that Parts Lookup often lists more than one model number for a single entry. Below is a listing copied directly from the Parts Lookup site, but edited to show only those models which I found having twin engines in them. I did not include single cylinder motors or diesel engined models in the list, and the ID Tag information is included for reference.
Again, I hope this helps.
From Parts Lookup (emphasis added):
Opposed Twin Cylinder Kohler Motors in:
1535 S/N 800,000 - 821,059, 141-641-100, 140-641-100
1541 S/N 800,000 - 816,508, 141-651-100, 140-651-100
1541 S/N 816,509 - 821,059, 141-652-100
1710, 682, 142-682-100, 2050584U, 682, 145-682-399, 145-682-100, 143-682-100, 144-682-100, 143-682-399, 205-0600, 142-682-399,
1710, 144-682-399, 2050600U, 2050592U, 2050593U
1711, 1712, 782, 784, 784142, 784, 782, 143-784-399, 1711, 1712, 143-784-100, 142-784-100, 784143, 142-784-399, 145-782-100, 145-784-100, 144-784-100, 2050585U, 2050601U, 2050594U, 142-782-100, 143-782-100, 144-782-100
1806 S/N 756,300 - 799,999, 147-640-100, 148-640-100, 149-640-100
1810 S/N 756,300 - 799,999, 147-650-100, 148-650-100, 149-650-100, 146-682-100
1811 & 1812 S/N 756,300 - 799,999, 148-660-100, 147-670-100, 1811 S/N 756,300 - 799,999, 147-660-100, 146-782-100, 147-720-100, 148-670-100, 149-670-100, 146-784-100, 149-660-100, 1812 S/N 756,300 - 799,999
1860 S/N 800,000 - 821,059, 141-661-100, 140-661-100
1861 S/N 821,060 - 836,000, 142-663-100, 140-671-100
1862 S/N 800,000 - 821,059, 140-681-100, 141-681-100
1862 S/N 821,060 - 836,000, 142-683-100
<font size="+2">Opposed Twin Cylinder Briggs & Stratton Motors in:</font>
1604, 1606, 580, 582, 2050598U, 582, 1604, 144-582-399, 145-582-399, 142-582-399, 142-582-100, 143-582-100, 144-582-100, 205-0582, 1606, 145-580-100, 144-580-100, 143-582-399, 580, 143-580-100, 142-580-100, 146-580-100, 2050599U, 2050596U, 2050582U, 2050583U, 145-582-100, 146-582-100
V-Twin Motors in:
1641 S/N 821,060 - 880,000, 142-653-100, 145-653-100, 144-653-100, 143-653-100
1641 S/N 880,001 - 899,000, 14A-653-100, 146-653-100
1863 S/N 836,001 - 880,000, 145-664-100, 144-664-100, 143-664-100
1863 S/N 880,001 - 899,000, 14A-664-100, 146-664-100
1864 S/N 836,001 - 880,000, 144-684-100, 145-684-100, 143-684-100
1864 S/N 880,001 - 899,000, 14A-684-100, 146-684-100
Engine Disclaimer: The engine horsepower information is provided by the engine manufacturer to be used for comparison purposes only. See your local Cub Cadet Independent Dealer for warranty details.
I left the HP disclaimer in because it cracks me up every time I see it.