Greatest Common Factor (GCF) and Least Common Multiple (LCM)

LCM Word Problem

At a family reunion, each of Dakota's aunts and uncles is getting photographed once. The aunts are taking pictures in groups of 12 and the uncles are taking pictures in groups of 20. If Dakota has the same total number of aunts and uncles, what is the minimum number of aunts that Dakota must have?

GCF Word Problem

Avery gets newsletters by e-mail. He gets one for sports every 6 days, one for model railroads every 10 days, and one for music every 3 days. If he got all three today, how many more days will it be until he gets all three newsletters on the same day again?

4

GCF of 12 and 20

1

GCF of 2 and 7

1

GCF of 5 and 4

2

GCF of 6 and 10

6

GCF of 6 and 12

4

GCF of 8 and 12

3

GCF of 9 and 6

2x2x2x3x4

Prime Factorization of 120

2x2x5x7

Prime Factorization of 140

2x2x3x3x7

Prime Factorization of 252

2x2x2x2x2

Prime Factorization of 32

Least Common Multiple

The smallest number that is a product of both numbers being compared (can be one of the numbers, can't be smaller than both numbers)

Factor

one of 2 numbers that multiplied together gives a product

Greatest

the largest value; "biggest"

Multiple

the product of 2 numbers

Least

the smallest value

60

LCM 12 and 20

24

LCM of 12 and 24

14

LCM of 2 and 7

20

LCM of 5 and 4

30

LCM of 6 and 10

12

LCM of 6 and 12

24

LCM of 8 and 12

35

Mike notices that his apartment number is divisible by 7, and his sister notices it is divisible by 5. What is the smallest possible apartment number?

2x2x3x3

Prime Factorization of 36

3x3x3x3x5

Prime Factorization of 405

2x2x2x2x5

Prime Factorization of 80

5x5x5x7

Prime Factorization of 875

Greatest Common Factor

The largest numbers that is a factor for both the numbers being compared (can be one, can't be bigger than either number)