Least Common Factors and Greatest Common Factors

Greatest Common Factor and Least Common Multiple

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Objectives

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• Determine the Greatest Common Factor (GCF) of two or more numbers.

• Determine the Least Common Multiple (LCM) of two or more numbers.

• Solve real-life problems involving GCF and LCM.

Multiple Choice

A ______ is a quantity that divides another quantity evenly.

• Factor

• Multiple

• Greatest Common Factor

• Least Common Multiple

Multiple Choice

A ______ is a product obtained by multiplying a number by a natural number.

• Factor

• Multiple

• Greatest Common Factor

• Least Common Multiple

Greatest Common Factor

The greatest common factor (GCF) of two or more numbers is the largest number that divides the given numbers evenly.

What is the GCF of 12 and 16?

Solution:

​12: (on a piece of paper, or in your head if you can, list all the factors of 12 in order, starting with 1, making sure each factor can fit inside of 12 evenly with no remainders)

16: ​ (do the same thing with the number 16)

GCF: look for the largest factor they have in common. That is the GCF!​

What is the GCF of 24 and 36?

Solution:

What is the GCF of 48, 60, and 96?

Solution:

Fill in the Blank

What is the GCF of 39 and 65?

Fill in the Blank

What is the GCF of 91 and 112?

Fill in the Blank

What is the GCF of 36, 84, and 132?

Fill in the Blank

Jefty has two pieces of cloth, which will be used for a decoration. One piece is 72 inches wide and the other piece is 90 inches wide. He wants to cut the cloths into strips of equal widths as wide as possible. How wide should he cut the cloths?

Fill in the Blank

Project 360 Organization has 96 boxes of crayons, 144 pieces of pencil, and 192 pads of paper, which will be donated to its adopted day care center. If the children should receive the same number of boxes of crayons, pieces of pencils, and pads of paper, how many children are there in the center?

Least Common Multiple

The least common multiple (LCM) of two or more numbers is the smallest natural number that is a multiple of the given numbers.

What is the LCM of 14 and 21?

Solution:

What is the LCM of 6 and 15?

Solution:

What is the LCM of 3, 8, and 9?

Solution:

Fill in the Blank

What is the LCM of 8 and 14?

Fill in the Blank

What is the LCM of 18 and 28?

Fill in the Blank

What is the LCM of 7, 12, and 15?

Fill in the Blank

A signal light panel board has 3 blinker bulbs that blink in 3 different time intervals. The red light blinks every 2 seconds. The blue light blinks every 3 seconds. The yellow light blinks every 4 seconds. In how many seconds will the three lights flash together?

Fill in the Blank

The SLSI cafeteria serves burger every 10 days and fries every 15 days. If both burger and fries are served today, when will these food be served together again?

Open Ended

In your own words, describe what you learned or what may have confused you. If you were confused, please be specific about what was hard for you to understand.