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There are several variants of the notation for multiplication:

$n \times m$

This is usually used when numbers are under consideration, for example: $3 \times 5 = 15$.

However, it can be used in the context of algebra where extra clarity is needed.

$n m$

This is most common in algebra, but not with numbers, as it is difficult to make it obvious where one number ends and the next number begins.

$\paren n \paren m$

This form can be used for either symbols denoting variables or numbers, for example: $\paren 3 \paren 4 = 12$.

$n \cdot m$ or $n . m$

These have their uses in algebra, but the dot has the danger of being confused with the decimal point when used for numbers.

$n * m$

This notation specifically evolved in the field of computer science, but can occasionally be seen encroaching into mathematics.

Its use is not recommended, as it can be confused with other operations that use the same or similar notation, for example convolution.