A 30 m, 36 m, and 84 m wire are to be cut into equal pieces. What is the least number of pieces the wires can be cut into?

This will be the length of the longest possible equal pieces.
Prime factorization of each length:

The common prime factors are 2 and 3.
The lowest power of 2 is $2^1$.
The lowest power of 3 is $3^1$.

So, each piece of wire will be 6 meters long.

Number of pieces from the 30 m wire = $\frac{30}{6} = 5$ pieces
Number of pieces from the 36 m wire = $\frac{36}{6} = 6$ pieces
Number of pieces from the 84 m wire = $\frac{84}{6} = 14$ pieces

Total pieces = $5 + 6 + 14 = 25$ pieces