1. Least common multiple of three numbers

2. L.C.M is the Smallest number that a set of given numbers
divides evenly into
It is useful to know how to do this so you can find a common
denominator when adding or subtracting or ordering fractions.
Least common multiple of three numbers can be calculated
using two methods
Prime factorization
Ladder Method or L Method

3. Example1: Find L.C.M of 6 , 12 , 15
Solution Method 1:- Prime Factorization Method
Step1:- Find prime factorization of 6 , 12 and 15 12 15 6 2 6 3 5 2 3 2 3
6 = 2 x 3
12 = 2 x 2 x 3
15 = 3 x 5
Step2:- Write down product of all the common factors
Step 3:- Write down product of all remaining factors
L.C.M = 2
x 3
x 2
x 5
= 60

4. Solution Method 2:- L Method
Step1:- Use L Method to find factors of 6 , 12 and 15 3
Common
Factors
Once 2
Step2:- Write down product of all the common factors
Step 3:- Write down product of all remaining factors
Remaining Factors
L.C.M = 3
x 2
x 1
x 2
x 5
= 60

5. Example2: Find L.C.M of 18 , 24 , 60
Solution Method 1:- Prime Factorization Method
Step1:- Find prime factorization of 18 , 24 , 60 24 60 18 2 12 2 30 2 9 2 6 2 15 3 3 2 3 3 5
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5

6. 18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
Step2:- Write down product of all the common factors
Step 3:- Write down product of all remaining factors
L.C.M = 2
x 3
x 2
x 3
x 2
x 5
= 360

7. Solution Method 2:- L Method
Step1:- Use L Method to find factors of 18 , 24 , 60 2
Common
Factors
Once 3 2
Remaining Factors
Step2:- Write down product of all the common factors
Step 3:- Write down product of all remaining factors
L.C.M = 2
x 3
x 2
x 3 x 2
x 5
= 360

8. Try these
Find L.C.M of 36 , 18, 9
Find L.C.M of 20 , 30, 50