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Question

Find Least Common Multiple of 12, 24, 48, 60 and 96 using prime factorisation method.

Answer

LCM( 12, 24, 48, 60, 96 ) = 480

Explanation

Step 1: Write down factorisation of each number:

12 = 2 · 2 · 3

24 = 2 · 2 · 2 · 3

48 = 2 · 2 · 2 · 2 · 3

60 = 2 · 2 · 3 · 5

96 = 2 · 2 · 2 · 2 · 2 · 3

Step 2 : Match primes vertically:

12=2·2·      3  
24=2·2·2·    3  
48=2·2·2·2·  3  
60=2·2·      3·5
96=2·2·2·2·2·3  

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

12=2·2·      3    
24=2·2·2·    3    
48=2·2·2·2·  3    
60=2·2·      3·5  
96=2·2·2·2·2·3    
LCM=2·2·2·2·2·3·5=480
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