GCF AND LCM

•What is the greatest common factor (GCF) of two numbers?

•When is the GCF useful?

•The biggest number that can evenly divide both.

•When we are trying to reduce a fraction.

•What is the simplest form of ?

•Divide the numerator and the denominator by their GCF.

310

290

31

29

10310

10290

•What is the Least Common Multiple (LCM) of two numbers?

•The smallest number that can be evenly divided by both numbers.

•When is the LCM useful?

•When finding a new common denominator for fractions so they may be compared, added, or subtracted.

•What is the LCM of 4, 6, and 8?

•List out multiples of all numbers:

•4: 4, 8, 12, 16, 20, 246: 6, 12, 18, 248: 8, 16, 24

•The first number on all lists is the LCM, so 24

Collaborative Station: GCF• You and your partner will each have a number. Both of

you will find the prime factorization of your number.• By comparing both of your prime factorizations, you will

be able to find the GCF of your two numbers.

Collaborative Station: GCF Example• Partner A’s number is 84. He draws a factor tree and

figures out that the prime factorization of 84 is 2×2×3×7• Partner B’s number is 60. She draws a factor tree and

figures out that the prime factorization of 60 is 2×2×3×5• Once both partners are done, they copy down their

partner’s prime factorization onto their own paper.• Comparing the prime factorizations, the partners see that

both have 2, 2, and 3 in common.• Both partners write: The GCF of 84 and 60 is 2×2×3 = 12

Independent Station: Reducing Fractions

• We will find the fully reduced form of fractions by finding the GCF of the numerator and denominator, then dividing by that number.

• Example: Reduce the fraction 4/8• On your paper, you will find the GCF of 4 and 8, which is

4.• Divide the numerator and denominator by the GCF to get

the fully reduced fraction.