1. Least Common Multiples (LCM) & Greatest Common Factors (GCF)
I will find LCM and GCF of two numbers by listing factors and multiples.

2. Vocabulary Factor Greatest Common Factor
The numbers multiplied together to get a product.
Greatest Common Factor
The largest factor that is the same between two numbers.
Example:
Factors of 4: 1, 2, 4
Factors of 12: 1, 2, 3, 4, 6, 12
The GCF is 4.

3. Ladder Method For GCF Write both numbers on the same line
Draw an “L” or upside down division symbol
Divide the same number into both numbers inside the “L”
Continue to divide into the numbers until you can’t anymore
Multiply the numbers down the LEFT side
This is your GCF
Video:

4. It’s that easy! Let’s try some together.
The greatest common factor of 8 and 10.
GCF of 9 and 26.
GCF of 20 and 45.

5. Vocabulary Multiple Least Common Multiple
The product of the number and any nonzero whole number
Least Common Multiple
The smallest multiple that is the same between two numbers.
Example:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32
Multiples of 12: 12, 24, 36, 48

6. Ladder Method For LCM Write both numbers on the same line
Draw an “L” or upside down division symbol
Divide the same number into both numbers inside the “L”
Continue to divide into the numbers until you can’t anymore
Multiply the numbers down the LEFT side AND BOTTOM
This is your LCM
Video:

7. It’s that easy! Let’s try some together.
Least Common Multiple of 5 and 2
LCM of 12 and 8
LCM of 9 and 3

8. Finding the LCM of 3 or more numbers
Put the numbers in the ladder as before.
When you can NO longer divide into ALL numbers with the SAME divisor, STOP!
This will be your GCF, multiply the numbers down the LEFT side.
To find the LCM, continue to divide UNTIL you have ALL prime numbers and/or 1’s.
If the divisor does NOT go into one of the numbers, simply BRING IT DOWN!
You also can NOT have any duplicate numbers.
Divide by the duplicate numbers to get rid of them.

9. Example 14 20 30 28 7 does not go into 2 or 3, just BRING THEM DOWN!
5 does not go into 7 or 14 , just BRING THEM DOWN!
7 does not go into 2 or 3, just BRING THEM DOWN!
There are duplicate 2’s, so divide by 2 to get rid of them—2 doesn’t go into 1 or 3, so just bring them down.