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Find Least Common Multiple of 299 and 256 using prime factorisation method.

Answer

LCM( 299, 256 ) = 76544

Explanation

Step 1: Write down factorisation of each number:

299 = 13 · 23

256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

299=                13·23
256=2·2·2·2·2·2·2·2    

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

299=                13·23  
256=2·2·2·2·2·2·2·2      
LCM=2·2·2·2·2·2·2·2·13·23=76544

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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