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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?

- 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.

- 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

- 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.