# Finding the LCM & GCF 24 126 36

```Finding the LCM & GCF
LCM {Least Common Multiple}
GCF {Greatest Common Factor}
Use to find common denominator
Use to reduce fractions
Find the LCM for 24, 36, and 50
Find the GCF for 126 and 180
Step 1: Find the Prime Factorization of each number
Step 1: Find the Prime Factorization of both numbers
24
36
50
9
3
3
1
1
90
63
25
45
21
5
15
7
1
5
1
Step 2: Place the Prime Factors in a Box
24
36
50
0
8
1
2 2 3 3 5
6
180
6
2
1
2 3 3 7
18
0
5
2 5 5
6
3
2 2 3 3
4
2
2 2 2 3
12
126
2
3
2·2·2
2·2
2
3
3·3
Step 2:
1
Place the Prime factors in a Box
5
126
180
2
3
2
2·2
3·3
3·3
5
7
7
5
5·5
Step 3: Circle the greatest amount of times each prime factor occurs,
Step 3: Circle the least amount of times each prime factor occurs,
even if the factor is not common to all three numbers.
But the factors must be common to both numbers!
Note: 24 and 35 do not have 5 as a common factor, but 50 does so, we circle the 5’s also.
Saved: San Eil (Math Handout) LCM-GCF & EPCC (Math Emporium) HANDOUT LCM-GCF
So, do not use (5) or (7) because they are not common to both 126 and 180
1
```

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