# Lesson 95 – Doodles Do Algebra

Today we start learning about Least Common Multiple.

The Least Common Multiple is the least quantity that will exactly contain two or more other quanities. This means you can divide the least common multiple by any of the other quanities and there will be no remainder.

DoodleOne gives examples of 2, 3, and 6 that have a least common multiple of 6. You find it by multiplying together all the primes in all the quanities.

The best way to keep track is in a table.

Example:

So the least common multiple of ax, bx, and abc look like

prime              first quantity              second quantity              third quantity

ax              bx              abc

a              factor this out where you can and you get…

x              bx              bc

x              factor this out where you can and you get…

1              b              bc

b              factor this out where you can and you get…

1              1              c

c              factor this out where you can and you get…

1              1              1

now you have the first column with all the primes. The Least Common Multiple is all those primes multiplied together: axbc.

1.

prime              first quantity              second quantity              third quantity

$4a^2$              $3a^3x$              $6ax^2y^3$

3              factor this out where you can and you get…

$4a^2$              $a^3x$              $2ax^2y^3$

2              factor this out where you can and you get…

$2a^2$              $a^3x$              $ax^2y^3$

2              factor this out where you can and you get…

$a^2$              $a^3x$              $ax^2y^3$

a              factor this out where you can and you get…

$a$              $a^2x$              $x^2y^3$

a              factor this out where you can and you get…

$1$              $ax$              $x^2y^3$

a              factor this out where you can and you get…

$1$              $x$              $x^2y^3$

x              factor this out where you can and you get…

$1$              $1$              $xy^3$

x              factor this out where you can and you get…

$1$              $1$              $y^3$

y              factor this out where you can and you get…

$1$              $1$              $y^2$

y              factor this out where you can and you get…

$1$              $1$              $y$

y              factor this out where you can and you get…

$1$              $1$              $1$

So the Least Common Multiple is $3*2*2*a*a*a*x*x*y*y*y=12a^3x^2y^3$

2. $2*2*2*3*a*a*a*x*x*x*x*y*y=24a^3x^4y^2$

3. $2*2*3*3*c*c*c*n*n*n*n*x*x*x*z=36c^3n^4x^3z$

4. $2*3*3*5*c*x*x*x*z*z*z*z=60cx^3z^4$