Here are some words that rhyme or nearly rhyme with "problem":

• Column
• Solemn
• Slalom
• Bottom
• Common
• Cotton
• Fallen
• Forgotten
• Garden
• Often
• Foreign
• Awesome
• Option
• Prism
• Salem
• Atom
• Income
• Hoodlum
• Succumb
• Emblem
• Ransom
• Villain
• Stolen
• Golem

Note that some of these are near rhymes, meaning they dont perfectly rhyme with "problem" but have similar sounds.