SOLUTION: A fellow Intermediate Algebra student tells you that x ^2 y^2, x^5 y^5, x^3 y^3 and has a least Common Multiple [which is the LCM. but can be thought of as the Least Common Denomin

Algebra ->  Real-numbers -> SOLUTION: A fellow Intermediate Algebra student tells you that x ^2 y^2, x^5 y^5, x^3 y^3 and has a least Common Multiple [which is the LCM. but can be thought of as the Least Common Denomin      Log On


   



Question 1134145: A fellow Intermediate Algebra student tells you that x ^2 y^2, x^5 y^5, x^3 y^3 and has a least Common Multiple [which is the LCM. but can be thought of as the Least Common Denominator if it was the bottom of fractions]. You know that this student is INCORRECT Explain what the LCM really is for these terms and explain why or how you got that.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

x+%5E2%2A+y%5E2,+x%5E5+%2Ay%5E5, x%5E3+%2Ay%5E3
factor each term:
x+%5E2%2A+y%5E2=x%2Ax%2Ay%2Ay
+x%5E5+%2Ay%5E5=x%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay
x%5E3+%2Ay%5E3=x%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay
x: 5 occurrences
y: 5 occurrences
so,
LCM is +x%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%2Ay%2Ay
LCM=x%5E5%2A+y%5E5
since the LCM is the smallest integer that is evenly divisible by all given terms, you can check it this way:
+%28x%5E5+%2Ay%5E5%29%2F%28x+%5E2%2A+y%5E2%29=x%5E%285-2%29%2Ay%5E%285-2%29=x%5E3%2Ay%5E3
+%28x%5E5+%2Ay%5E5%29%2F%28x+%5E3%2A+y%5E3%29=x%5E%285-3%29%2Ay%5E%285-3%29=x%5E2%2Ay%5E2