1. Unit 1; Part 2: Using Factors for Fractions and Solving Problems
You need to be able to find
the GCF, LCM and solve
problems using them.

2. Advanced Homework Answers pp. 222-223 % % % %
/80
44. C
52. –83 %
45. G
students %
points % % % %

3. CHECK CHAPTER % FOR LAST YEARS SHOW. THERE WERE CHANGES!!!!

4. Unit 1, Lesson 10 Advanced – LCM (least common multiple)
Assignment – p. 226;
#8-18 even (also find GCF) &

6. LCM Multiples are any number multiplied by 1, 2, 3, etc.
Multiples of 12: 12, 24, 36, 48, 60…
Multiples get bigger where factors get smaller.
Factors of 12: 1, 2, 3, 4, 6, 12

7. LCM
Least common multiple (LCM) is the smallest common multiple of 2 or more original numbers.
This is used to find the least common denominator. (Oh, boy. Can’t wait to that! Yuck!!!)
So, use LCM to find LCD.

8. LCM THE GCF of 2 or more numbers with nothing in common, is always 1.
The LCM of 2 or more numbers with nothing in common is found by simply multiplying them together.

9. LCM Find the GCF and LCM of 7 and 25. There are no common factors, so…

10. LCM
The LCM of 2 numbers with common factors is done exactly the same as GCF, using the same ladder as before.
The GCF is the numbers down the left side multiplied together just like before.

11. LCM
The LCM is all the numbers on the side and across the bottom multiplied together.
Down the side and across the bottom form a big L for LCM.

12. GCF and LCM 24 60 12 30 6 15 2 5 ) 2 ) 2 ) 3 LCM= 2x2x3x2x5=120
GCF= 2x2x3=12

13. GCF and LCM ) 2 ) 3
GCF=2x3=6
LCM=2x3x50x3=900

14. GCF and LCM ) 5
GCF=5
LCM=5x125x6=3750

15. GCF and LCM of 3 Numbers The GCF works the same way with 3 numbers.
You are done when there are no common factors for ALL 3 numbers.

16. GCF and LCM of 3 Numbers ) 2 ) 3
GCF=2x3=6

17. GCF and LCM of 3 Numbers 18 42 60 9 21 30 3 7 10 ) 2 ) 3
Since the bottom numbers have nothing in common, this example works the same as before.
LCM=2x3x3x7x10=1260

18. GCF and LCM of 3 Numbers 56 14 70 28 7 35 4 1 5 ) 2 ) 7 GCF=2x7=14
LCM=14x20=280

19. GCF and LCM of 3 Numbers
If there are any repeated factors on the bottom, you must do some additional work to find the LCM.
BUT, you first need to figure the GCF, since the common factors must be from all three numbers.

20. GCF and LCM of 3 Numbers 200 120 180 100 60 90 50 30 45 10 6 15 ) 2 )
GCF=2x2x5=20

21. GCF and LCM of 3 Numbers After you find the GCF:
Keep dividing by factors that are common to 2 of the 3 numbers.
The 3rd number that can’t be divided is brought down as is.
Keep going until there are no common factors at all.
The LCM is the product of all the numbers (side and bottom).

22. GCF and LCM of 3 Numbers ) 2 ) 2
LCM=
2x2x5x2x3x5x1x3
=1800 ) 5 ) 2 ) 3

23. GCF and LCM of 3 Numbers 12 18 28 6 9 14 3 9 7 1 3 7 ) 2 ) 2 ) 3 GCF=2
LCM=2x2x3x1x3x7=252

24. GCF and LCM of 3 Numbers ) 2 ) 2 ) 2 ) 2 ) 2
GCF=24=16
LCM=25x1x5x3=252

25. You may only work with 2 out of 3 numbers on LCM.
GCF and LCM of 3 Numbers
REMEMBER!!!!!!
You may only work with 2 out of 3 numbers on LCM.
GCF MUST be all 3 numbers.

26. LCM
Find the GCF and LCM of 12 and 15.

27. LCM
Find the GCF and LCM of 3 and 15.

28. LCM
Find the GCF and LCM of 60 and 80.

29. LCM
Find the GCF and LCM of 24 and 36.

30. LCM Find the GCF and LCM of 2, 3 & 49.
There are no common factors, so…
GCF = 1 and
LCM = 2(3)(49) = 294

31. LCM
Find the GCF and LCM of 2, 6 and 10.

32. LCM
Find the GCF and LCM of 18, 42 & 60.

33. LCM Be careful when doing 3 numbers! Check the numbers at the bottom.
Do they have ANY common factors? (doesn’t have to be in all 3)

34. LCM
If so:
Find the GCF on the side. (The ones that went into all three.)
Write it down now!
Don’t wait until the end.

35. LCM
Then keep dividing by factors that are common to 2 of the 3 numbers.
The 3rd number that can’t be divided is brought down as is.
Keep going until there are no common factors at all. The LCM is the product of all the numbers (the L on the side and bottom).

36. LCM
Find the GCF and LCM of 4, 10 and 9.

37. LCM
Find the GCF and LCM of 10, 12 & 15.

38. LCM
Find the GCF & LCM of 200, 120 & 180.

39. End of Slide Show

40. End of Lesson 7

41. Advanced Homework Answers p. 226
8. GCF=2; LCM=24
10. GCF=15; LCM=90
/25
12. GCF=1; LCM=132
30. 1/5
14. GCF=1; LCM=30
31. 3/25
16. GCF=4; LCM=48
18. GCF=11; LCM=132