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Question

Find Least Common Multiple of 44, 72, 108, 144 and 88 using prime factorisation method.

Answer

LCM( 44, 72, 108, 144, 88 ) = 4752

Explanation

Step 1: Write down factorisation of each number:

44 = 2 · 2 · 11

72 = 2 · 2 · 2 · 3 · 3

108 = 2 · 2 · 3 · 3 · 3

144 = 2 · 2 · 2 · 2 · 3 · 3

88 = 2 · 2 · 2 · 11

Step 2 : Match primes vertically:

44=2·2·          11
72=2·2·2·  3·3    
108=2·2·    3·3·3  
144=2·2·2·2·3·3    
88=2·2·2·        11

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

44=2·2·          11  
72=2·2·2·  3·3      
108=2·2·    3·3·3    
144=2·2·2·2·3·3      
88=2·2·2·        11  
LCM=2·2·2·2·3·3·3·11=4752
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