3x^2, 12y, and 10x^3y^3
what is the lcm of these numbers?
More importantly how do you figure out the answer if it is a question with this many powers?
do just like you would with numbers, break them down into prime factors. Then "collect" them so all are represented.
3x^2 = 3*x*x
12y = 3*2*2*y
10x^3y^3 = 2*5*x*x*x*y*y*y
so we need: 2*2*3*5*x*x*x*y*y*y
= 60x^3y^3
To find the least common multiple (LCM) of these expressions, we need to determine the highest power of each variable that appears in any of the expressions. Let's break it down:
Expressions:
1. 3x^2
2. 12y
3. 10x^3y^3
Now, let's examine each expression separately:
1. The expression 3x^2 includes the variables x^2. Since this is the highest power of x among all the expressions, we need to account for it.
2. The expression 12y does not contain any x variables but has a y variable. Therefore, we consider the variable y in this expression.
3. The expression 10x^3y^3 contains both x and y variables. Since this expression has the highest powers of both variables among the three expressions, we need to consider both.
Now, let's determine the highest powers for each variable:
For x:
- The highest power of x is x^3, which appears in the expression 10x^3y^3.
For y:
- The highest power of y is y^3, which also appears in the expression 10x^3y^3.
Therefore, to find the LCM of these expressions, we take the highest powers of each variable, resulting in:
LCM = x^3y^3
So, the least common multiple of 3x^2, 12y, and 10x^3y^3 is x^3y^3.