Bring a large pot of salted water to a boil and cook the linguine according to package directions; drain and keep warm.
In a large saucepan over medium heat, melt the butter until foaming.
Add the smashed garlic cloves and sauté in the butter until softened and fragrant, about 1–2 minutes.
Use a slotted spoon to remove and discard the garlic pieces, leaving the flavored butter in the pan.
Stir in the chopped parsley, then whisk in the all-purpose flour until combined.
Slowly whisk in the half and half, then add the chopped clams and about the juice of 2½ cans; add a couple teaspoons of lemon juice to start.
Cook, stirring frequently over medium heat, until the sauce is hot and slightly thickened, about 3–5 minutes; adjust lemon and seasoning to taste.
Toss the cooked linguine with the clam sauce until evenly coated and serve immediately.