# Lowest Common Multiple – Peg Board

DW has been working out knowing primes, multiples, and how numbers can be friends at different points in the number line.  Today we began discussing factors and multiples.

FACTOR  x  FACTOR = MULTIPLE – just so we are on the same page with our terms.

We began discussing when certain factors would come up with the same multiple – for example 6 and 4 have 12, 24, and 48 among others.  We then discussed it would be great if we could find out what the first time say 6 and 10 have the same multiple.

We started out with smaller numbers and soon began doing larger ones.  (I remember doing this with BR and another child in the classroom several years ago and they kept picking at least one prime number for the pair. Frustating.)

Least Common Multiple with the Peg Board

At the top of the peg board write the numerals 6 and 10.  These will define the two columns.

Choose one color of pegs for the 6 and one for the 10.  Place six pegs under the 6 and ten pegs under the 10.  Cut two pieces of yarn and place one under the six beads and one under the ten beads. This indicates one group of each.

We are going to keep counting out the multiples in each column until the rows are equal.  Place the pegs in the board again. Cut more yarn.  Keep going.

Continue adding to the smaller column if the rows don’t stay sort of even.

Once the amounts are the same in each column (at 30) write down the groups.

6 x 5 = 30 and 10 x 3 = 30

Try it again.