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Question

Find Least Common Multiple of 27, 32, 60, 90 and 132 using prime factorisation method.

Answer

LCM( 27, 32, 60, 90, 132 ) = 47520

Explanation

Step 1: Write down factorisation of each number:

27 = 3 · 3 · 3

32 = 2 · 2 · 2 · 2 · 2

60 = 2 · 2 · 3 · 5

90 = 2 · 3 · 3 · 5

132 = 2 · 2 · 3 · 11

Step 2 : Match primes vertically:

27=          3·3·3    
32=2·2·2·2·2          
60=2·2·      3·    5  
90=2·        3·3·  5  
132=2·2·      3·      11

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

27=          3·3·3      
32=2·2·2·2·2            
60=2·2·      3·    5    
90=2·        3·3·  5    
132=2·2·      3·      11  
LCM=2·2·2·2·2·3·3·3·5·11=47520
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