Different Cassette?

[SadieKate]

I assume this is a 9 spd bike? Because that what my answer assumes. . .

You need to know what kind of rear derailleur you have (short, med or long cage). Since you have a triple, you probably have a rear derailleur that can handle up to a 27 Shimano cassette or maybe a 28 SRAM 9 (about one more gear than you have now). If you swap the rear der to a Shimano XT, you can put on a Shimano or SRAM cassette with a large cog of 32 or 34 (about 3 to 4 gears lower than currently).

You will need a new chain to accomodate the larger cassette no matter what. So determine your rear derailleur's capacity and then choose a cassette to match, or budget in a new rear derailleur also.

Editing -- I'm taking almost everything back that I said above because the bike is a 10 spd. You can put on a 28 SRAM 10-spd cassette. I didn't look at the rear derailleur specs, but you need to be sure the cage will handle the larger cassette.