They both played lead guitar only a few months in that band.
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Page, Beck, and Clapton were all with the band for over a year. Clapton and Page, around two years. The shortest stint was Beck’s. Page originally played bass with the band.
Page was one of the busiest session musicians in Britain in the early to mid 60s, played on a lot of records that don’t even sound remotely like Led Zeppelin or the Yardbirds. Same for John Paul Jones.