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Question

Find Least Common Multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 and 17 using prime factorisation method.

Answer

LCM( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 ) = 12252240

Explanation

Step 1: Write down factorisation of each number:

1 = 1

2 = 2

3 = 3

4 = 2 · 2

5 = 5

6 = 2 · 3

7 = 7

8 = 2 · 2 · 2

9 = 3 · 3

10 = 2 · 5

11 = 11

12 = 2 · 2 · 3

13 = 13

14 = 2 · 7

15 = 3 · 5

16 = 2 · 2 · 2 · 2

17 = 17

Step 2 : Match primes vertically:

1=1                      
2=  2                    
3=          3            
4=  2·2                  
5=              5        
6=  2·      3            
7=                7      
8=  2·2·2                
9=          3·3          
10=  2·          5        
11=                  11    
12=  2·2·    3            
13=                    13  
14=  2·            7      
15=          3·  5        
16=  2·2·2·2              
17=                      17

Step 3 : Bring down numbers in each column and multiply to get LCM:

1=1                        
2=  2                      
3=          3              
4=  2·2                    
5=              5          
6=  2·      3              
7=                7        
8=  2·2·2                  
9=          3·3            
10=  2·          5          
11=                  11      
12=  2·2·    3              
13=                    13    
14=  2·            7        
15=          3·  5          
16=  2·2·2·2                
17=                      17  
LCM=1·2·2·2·2·3·3·5·7·11·13·17=12252240
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