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Math 31 Activity # 7
“Greatest Common Factor and Least Common Denominator”
Your Name: ___________________
Finding Least Common Denominator (LCD):
Case 1) Denominators with no common factors. Example: Suppose denominators are:
a) 3, 8 What is LCD? ______
Explain how you found the LCD?
What is GCF?_______
Explain how you found the GCF?
b) 2 x , 3 t What is LCD? ______
What is GCF? ______
Develop the rules for finding LCD and GCF for expressions with no common factors.
a) In your own words provide a rule for finding least common denominator (LCD) when there are no common factors.
b) Set a rule for finding Greatest Common Factor (GCF) if the expressions have no common factors.
Case 2) One of the denominators is a multiple of the other(s).
Example: Suppose denominators are:
a) 2, 8
What is LCD?______
Explain how you found the LCD?
What is GCF? _____
Explain how you found the GCF?
b) ( x − 1 ), ( x − 1 )^2
What is LCD? _______
What is GCF? _______
Develop the rules for finding LCD and GCF for expressions if one of them is a multiple of the other(s).
a) In your own words provide a rule for finding least common denominator (LCD) when one denominator is a multiple of the other(s).
b) Set a rule for finding Greatest Common Factor (GCF) if one of the expressions is a multiple of the other(s).
Case 3) Denominators have some (but not all) factors in common.
For each of the following find both the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) [if it was in a fraction we would call it a LCD]. Do the work on your own paper and attach it to this page. Write the answers on this page.
GCF LCM
- 10t^5 , 15t^4 , and 25t^3
- x^5 y^2 , x^4 y^5 , x^3 y^3 , and x^2 y^3
- 4(x – 1) and 8(x – 1)
- x^2 + 3x + 2 and x^2 – 4
- y^3 – y^2 and y^4 – y^2
- 8x^3 z, 12xy^2 , and 4y^5 z^2
- x^2 – 9, x + 3, and (x – 3)^2
- 2x^2 + 5x + 2 and 2x^2 – x – 1
- a – 5 and (a^2 – 10a + 25)^2
- 9x^3 – 9x^2 – 18x and 6x^5 – 24x^4 + 24x^3
