How do I tell someone I think they have cancer?

I lost my mother when I was 14 years old to lung cancer. For the past 5 years I've lived with my little brother and step-mom. I'm unfortunately a night owl so I'm up when everyone else sleeps. Over the past few months, I've noticed that my step-mom coughs in her sleep the same way my mother did a few years before she was diagnosed with cancer.

My mom was diagnosed in stage 4, so it was too late for her, but I think if my step-mom was checked and diagnosed early she can be saved. I don't want my brother to lose his mother, how do I go about telling her I think she has cancer without sounding rude?
Updates
+1 y
Just information, yes, she is a smoker, for as long as I've known her (since I was a toddler), and it's roughly a pack every 2-3 days (down from a pack a day)
How do I tell someone I think they have cancer?
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