Question

How is the least common multiple determined for the two expressions?

Answer 1

The least common multiple of two numbers is the first number that can divide them

We have the terms

`25v^8u^4,10v^2u^6w^3`

We will find the least common multiple of 25 and 10

Since the multiples of 25 are

`25,50,75,100,\ldots`

Since the multiples of 10 are

`10,20,30,40,50,60,\ldots`

The first common multiple in both lists is 50, then

The least common multiple of 25 and 10 is 50

For the same variables, we will choose the greatest exponent

For v

`v^8,v^2\rightarrow v^8`

The least common multiple of v is v^8

For u

`u^4,u^6\rightarrow u^6`

The least common multiple of u is u^6

For w

`w^3\rightarrow w^3`

The least common multiple w is w^3

Then the least common multiple of the 2 terms is

`50v^8u^6w^3`