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Question

Find Least Common Multiple of 28, 36, 54, 72 and 144 using prime factorisation method.

Answer

LCM( 28, 36, 54, 72, 144 ) = 3024

Explanation

Step 1: Write down factorisation of each number:

28 = 2 · 2 · 7

36 = 2 · 2 · 3 · 3

54 = 2 · 3 · 3 · 3

72 = 2 · 2 · 2 · 3 · 3

144 = 2 · 2 · 2 · 2 · 3 · 3

Step 2 : Match primes vertically:

28=2·2·          7
36=2·2·    3·3    
54=2·      3·3·3  
72=2·2·2·  3·3    
144=2·2·2·2·3·3    

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

28=2·2·          7  
36=2·2·    3·3      
54=2·      3·3·3    
72=2·2·2·  3·3      
144=2·2·2·2·3·3      
LCM=2·2·2·2·3·3·3·7=3024
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