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There are several good ways to build rumble. I use a tanky mastery/rune setup which allows me to stack mostly ap right away and build into survival late.
My most common build is to get an amp tome first, and a potion. Next get a pair of boots lvl 1 and as fast as possible build up a deathfire grasp. start with kages pick first then go into the codex/grasp. As rumble you excell at killing enemies running away from you... but often times you're taking too much dmg to harrass hard enough to get them to run... so you can kill them! With deathfire grasp's short cooldown you can nuke someone down to lower their hp as a massive harass tool, which often sends them running. If they run they die, speed boost + flamethrower + harpoons secures the kill. After that its a toss up, but i like to go giants belt into rylais asap... after finishing off boots of course. If they're cc heavy get yourself merc treds if you ffind yourself getting mega fed 2 -3 kills right away, go with boots of swiftness.. the faster you are the more kills you're gonna get from runners.
After rylais.... well i rarely get a game that lasts that long but i like to build up a hextech revolver then go a hybrid route. hextech gunblade + guinsoo's rageblade if you're fed like mad, with abyssall cap to follow it all off, or go with more survive with sunfire/force of nature. If you wanna go more tanky, i recommend a randuin's omen. Builds some good surv and shuts down melee champs/great for team fight slows