1. L.C.M (Lowest Common Multiple) & G.C.F (Greatest Common Factor)

2. Finding Factors
Finding the factors of a number can be done by sequentially dividing numbers into the product. When the factors begin to repeat you have found all factors.

3. Lowest Common Multiple L.C.M.40 8 10
Take two numbers
If you do the times table for each at what number do they cross
The first time they cross is at 40
So it’s the Lowest Common Multiple
of these two numbers

4. Methods of finding L.C.M. Prime Factorization method
Express each of the numbers as a product of prime factors
Product of the terms containing the highest powers is taken to find the L.C.M.
Example:
Find the LCM of 36, 40 and 45

5. Methods of finding L.C.M. Common Division Method
Arrange the given numbers in a row
Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible.
The product of the divisors and the undivided numbers is the required L.C.M.
Find the LCM of 21, 28, 36

6. L.C.M. Practice Problems Find the LCM of the following :
9 , 15, 18, 20
21, 45, 63, 81
168, 392,
315, 405
48, 60, 72, 96
1071, 2601

7. Greatest Common Factor (G.C.F.)
The greatest common factor is the largest common factor of two numbers. Factors are all of the numbers that divide into a given number equally.
The greatest common factor can be found by comparing all the factors of two numbers or by finding the prime factorization of two numbers

8. Finding The G.C.F. Using Factors
Determine the greatest common factor of two numbers by finding all the factors for the two numbers then comparing them. The largest common factor of the two numbers is their greatest common factor.

9. G.C.F. Using Factors The greatest common factor is of 36 and 24 is 12
Find the G.C.F. of 36 and 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36
Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24
Common Factors of 36 and 24 are: 1,2,3,4,6,12
The greatest common factor is of 36 and 24 is 12

10. Finding the G.C.F. Using Prime Factorization
To determine the greatest common factor find the prime factorization for each number. Find all of the common prime factors of the two numbers and multiply them together. Your sum is the G.C.F.

11. G.C.F. Using Prime Factorization
Find the G.C.F. of 36 and 24
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36= 2×2×3× = 2×2×2×3
The G.C.F. of 36 and 24 is 2×2×3=12