Online College Courses for Credit

Lattice algorithm for multiplication

Lattice algorithm for multiplication


To master the lattice algorithm.

This packet is intended to be an introduction to the lattice multiplication algorithm. This algorithm is sometimes taught in elementary schools, but many adults are unfamiliar with it.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

27 Sophia partners guarantee credit transfer.

307 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 29 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.



The lattice algorithm is used for multiplying multi-digit numbers. Some important features of the algorithm include:

  • We do not pay attention to the values of the numbers as we work through the algorithm-only to the digits themselves,
  • We do all of the multiplications first, followed by the additions (in contrast to the standard algorithm), meaning...
  • There is no carrying in the multiplication phase of the algorithm, and
  • We have to take a little bit of time to set up the lattice before we can begin multiplying.

In this packet, I will solve two problems:

  1. A 2-digit by 2-digit problem, and
  2. A 3-digit by 2-digit problem


Two-digit by two-digit example

This video demonstrates the lattice algorithm with two two-digit numbers.

Three-digit by two-digit example

This video demonstrates the lattice algorithm with larger numbers.

Lattice v. standard algorithm smackdown

So you spend a lot of time setting up the lattice, right? It must take a lot longer than the standard algorithm, right?
Let's see.
I'll multiply two 10-digit numbers. Which will be completed first? And by how much?
(Note: While the video is sped up, it still takes two minutes...feel free to fast forward to the end!)