Least Common Multiple
1. List the prime factorization of each number using exponential notation.
2. List the factors of the LCM by including each prime factor that appears in any of the numbers the greatest number of times that it appears in any factor.
3. Write the result in standard notation.
Find the LCM for 15, 30, and 50:
15 = 3 (5) = 3 (5)
30 = 2 (3) (5) = 2 (3) (5)
50 = 2 (5) (5) = 2 (5)^2
LCM = 2 (3) (52) = 150
(LCM will have one factor of 2, one factor of 3, and two factors of 5)
2. List the factors of the LCM by including each prime factor that appears in any of the numbers the greatest number of times that it appears in any factor.
3. Write the result in standard notation.
Find the LCM for 15, 30, and 50:
15 = 3 (5) = 3 (5)
30 = 2 (3) (5) = 2 (3) (5)
50 = 2 (5) (5) = 2 (5)^2
LCM = 2 (3) (52) = 150
(LCM will have one factor of 2, one factor of 3, and two factors of 5)
Greatest Common Factor
1. List the prime factorization of each number in exponential notation.
2. The GCF includes factors common to each number the smallest number of times that each factor appears.
3. Write the result in standard notation.
Find the GCF for 15, 30, and 50:
15 = 3 (5) = 3 (5)
30 = 2 (3) (5) = 2 (3) (5)
50 = 2 (5) (5) = 2 (5)^2
GCF = 5
(GCF will have one factor of 5)
2. The GCF includes factors common to each number the smallest number of times that each factor appears.
3. Write the result in standard notation.
Find the GCF for 15, 30, and 50:
15 = 3 (5) = 3 (5)
30 = 2 (3) (5) = 2 (3) (5)
50 = 2 (5) (5) = 2 (5)^2
GCF = 5
(GCF will have one factor of 5)
Classwork/Extra Practice:
1) What is the least common multiple of 3 and 4?
2) What is the least common multiple of 12 and 18? 3) What is the least common multiple of 6 and 18? 4) What is the least common multiple of 3, 4, and 12? 5) What is the least common multiple of 8, 12, and 20? |
6) Find the greatest common factor of 18 and 20.
7) Find the greatest common factor of 15 and 22. 8) Find the greatest common factor of 10, 15, and 20. 9) Find the greatest common factor of 30 and 55. 10) Find the greatest common factor of 36, 72, and 144. 1-12 2-36 3-18 4-12 5-120
6-360 7-330 8-3,000 9-1,650 10-144 |
