Savage 12 LRP barrel swap

[XL105]

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[scooterf79]

You could measure your barrel and compare with the measurements of the barrel you're interested in. If yours is already a varmint contour you should be ok, and IIRC the LRP is....
Scooter

[XL105]

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[Newsshooter]

OEM barrel on the LRP is a large shank full bull, varmint is smaller.