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Question

Find Least Common Multiple of 18, 22, 56 and 64 using prime factorisation method.

Answer

LCM( 18, 22, 56, 64 ) = 44352

Explanation

Step 1: Write down factorisation of each number:

18 = 2 · 3 · 3

22 = 2 · 11

56 = 2 · 2 · 2 · 7

64 = 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

18=2·          3·3    
22=2·                11
56=2·2·2·          7  
64=2·2·2·2·2·2        

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

18=2·          3·3      
22=2·                11  
56=2·2·2·          7    
64=2·2·2·2·2·2          
LCM=2·2·2·2·2·2·3·3·7·11=44352
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