Write down pairs of numbers on index cards. The numbers should be small enough that your students can determine the least common multiple fairly easily.
Write the least common multiples that are the answers to your index cards on the board in a random order.
Arrange your class in two lines. Each line will be its own team. Give the first player in each line a fly swatter.
Read out the numbers on an index card and yell, "Go!" The two students with fly swatters must then race to the board in an attempt to be the first person to swat the correct answer first. Whoever does so earns a point for his team.
Continue playing until everyone has had at least one turn. The team with the highest score wins.
Divide your class into pairs (or one group of three if you have an odd number of students) and give each group a deck of cards.
Instruct the students to divide the cards evenly among themselves and their partners.
Tell the groups to turn over one card simultaneously. Whoever can state the correct least common multiple of those two cards earns a point. Whoever earns the most points within a certain time frame wins. Let face cards equal 10 and aces equal 1.