BUGFIX avoid silent overflow in lcm least common multiple function

[KlausC]

Solves #33911 .
Define new functions checked_lcm and widelcm analogously to checked_mul and widemul.

The behaviour of lcm is not changed, and the user can switch to the appropriate variant at his own discretion.

[StefanKarpinski]

The lcm function is so costly that making it checked by default seems reasonable to me. Similarly, I feel like explicitly widening before calling lcm would be more composable.

[KlausC]

So it would be ok to change lcm by using checked_mul internally and neither introduce widelcm nor checked_lcm.
To be honest, I think that is the best fix, but I wanted to avoid the "checking is too expensive" - discussion.

[StefanKarpinski]

It's all about context: checking is too expensive when you're doing i + j but when you're doing lcm(i, j) that's a totally different story—that's already a very expensive operation.

[KlausC]

As you can see, I retired the new functions and added the checked_mul to lcm. The widelcm function is probably not worth the effort. So what remains is the fix of the silent error in lcm.

[StefanKarpinski]

I think you can revert the changes to this file now.

[KlausC]

done

[StefanKarpinski]

Well, that's certainly a much simpler fix now 😁 👍 💯

[KlausC]

The last change fixes a gotcha in twiceprecision.jl, where lcm is expected to produce incorrect results (and not to throw an overflow exception).
A test case failed for this reason on 32-bit machines.
No other such uses of lcm were found in base or stdlib sources.

[KlausC]

is the being forgotten?

[StefanKarpinski]

Thanks for the reminder!