The Egyptians determined that you could successfully multiply numbers by taking numbers that add up to the first number multiplying each by the second and then adding them together. For example, to multiply 15 x 12, you would take number that add up to 15 such as 3, 5 and 7 and multiply the smaller numbers by 12. You get 3 x 12 = 36, 5 x 12 = 60 and 7 x 12 = 84. Add those three together and you have the answer for 15 x 12, which is 180.
One of the most popular ways for multiplication computation is the use of multiplication tables. The answer to the multiplication of integers are placed in a table where the x and y axis. If you wanted to know the answer to five times five, then you find point on the graph where the fives and the x and y axis converge.
The slide rule was a common method for computing multiplications that involved decimals prior to calculators. A slide rule is an instrument with numbers along the top and bottom with a centerpiece that is movable and also has numbers. The number lines are represented by the alphabet, such as A,B,C,and D-scale/ Multiplying two numbers involved movement of the slide to the appropriate section and the answer is in the D-scale.
When calculators and computers took off, algorithms were developed to help computer compute multiplication problems as fast as possible. Since computers can perform calculations in a fraction of a second, they can do complex multiplication of complex and large numbers quickly. Most computers multiply using the discrete Fourier transform, which decreases the computations needed for large numbers.