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Find Least Common Multiple of 96, 288 and 256 using prime factorisation method.

Answer

LCM( 96, 288, 256 ) = 2304

Explanation

Step 1: Write down factorisation of each number:

96 = 2 · 2 · 2 · 2 · 2 · 3

288 = 2 · 2 · 2 · 2 · 2 · 3 · 3

256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

96=2·2·2·2·2·      3  
288=2·2·2·2·2·      3·3
256=2·2·2·2·2·2·2·2    

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

96=2·2·2·2·2·      3    
288=2·2·2·2·2·      3·3  
256=2·2·2·2·2·2·2·2      
LCM=2·2·2·2·2·2·2·2·3·3=2304

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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