Here's one way to do it:
1. (L v M) & (L v ~S)
2. A -> ~L
3. A -> (~M v S) :. ~A
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4. L v (M & ~S) 1 Distribution
5. ~~L v (M & ~S) 4 Double Negation
6. ~L -> (M & ~S) 5 Material Implication
7. A -> (M & ~S) 2,6 Hypothetical Syllogism
8. A -> (~M v ~~S) 3 Double Negation
9. A -> ~(M & ~S) 8 De Morgan's Law
10. ~~(M & ~S) -> ~A 9 Transposition
11. (M & ~S) -> ~A 10 Double Negation
12. A -> ~A 7,11 Hypothetical Syllogism
13. ~A v ~A 12 Material Implication
14. ~A 13 Tautology