# GCF and LCM - PowerPoint PPT Presentation

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GCF and LCM. The biggest number that can evenly divide both. When we are trying to reduce a fraction. What is the greatest common factor (GCF) of two numbers ? When is the GCF useful?. D ivide the numerator and the denominator by their GCF. What is the simplest form of ?.

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GCF and LCM

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## GCF and LCM

• The biggest number that can evenly divide both.

• When we are trying to reduce a fraction.

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

• When is the GCF useful?

• Divide the numerator and the denominator by their GCF.

• What is the simplest form of ?

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

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

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

• When is the LCM useful?

• 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

• What is the LCM of 4, 6, and 8?

### 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.