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Question

Find Least Common Multiple of 414, 112 and 128 using prime factorisation method.

Answer

LCM( 414, 112, 128 ) = 185472

Explanation

Step 1: Write down factorisation of each number:

414 = 2 · 3 · 3 · 23

112 = 2 · 2 · 2 · 2 · 7

128 = 2 · 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

414=2·            3·3·  23
112=2·2·2·2·          7  
128=2·2·2·2·2·2·2        

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

414=2·            3·3·  23  
112=2·2·2·2·          7    
128=2·2·2·2·2·2·2          
LCM=2·2·2·2·2·2·2·3·3·7·23=185472

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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