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Question

Find Least Common Multiple of 124, 112 and 256 using prime factorisation method.

Answer

LCM( 124, 112, 256 ) = 55552

Explanation

Step 1: Write down factorisation of each number:

124 = 2 · 2 · 31

112 = 2 · 2 · 2 · 2 · 7

256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

124=2·2·              31
112=2·2·2·2·        7  
256=2·2·2·2·2·2·2·2    

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

124=2·2·              31  
112=2·2·2·2·        7    
256=2·2·2·2·2·2·2·2      
LCM=2·2·2·2·2·2·2·2·7·31=55552

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.

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