Seems to me that the least common multiple is the product of a list of factors that consists of each distinct 'prime' factor of both expressions, with each one listed with the highest power to which it appears in either expression.
I never tried this with algebraic expressions before. Let's see what comes out.
The 'prime' factors of (8x⁵y³v⁷) are 2³, x⁵, y³, and v⁷ .
The factors of (4y⁶v⁸) are 2², y⁶, and v⁸ .
Those are the factors that have t appear in the GCM.
So THAT has to be . . . 2³ · x⁵ · y⁶ · v⁸ , or
8 x⁵ y⁶ v⁸
