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Question

Find Least Common Multiple of 406, 348 and 256 using prime factorisation method.

Answer

LCM( 406, 348, 256 ) = 155904

Explanation

Step 1: Write down factorisation of each number:

406 = 2 · 7 · 29

348 = 2 · 2 · 3 · 29

256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

406=2·                7·29
348=2·2·            3·  29
256=2·2·2·2·2·2·2·2      

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

406=2·                7·29  
348=2·2·            3·  29  
256=2·2·2·2·2·2·2·2        
LCM=2·2·2·2·2·2·2·2·3·7·29=155904

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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