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Find Least Common Multiple of 256, 136 and 436 using prime factorisation method.

Answer

LCM( 256, 136, 436 ) = 474368

Explanation

Step 1: Write down factorisation of each number:

256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

136 = 2 · 2 · 2 · 17

436 = 2 · 2 · 109

Step 2 : Match primes vertically:

256=2·2·2·2·2·2·2·2    
136=2·2·2·          17  
436=2·2·              109

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

256=2·2·2·2·2·2·2·2      
136=2·2·2·          17    
436=2·2·              109  
LCM=2·2·2·2·2·2·2·2·17·109=474368

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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