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Question

Find Least Common Multiple of 512 and 320 using prime factorisation method.

Answer

LCM( 512, 320 ) = 2560

Explanation

Step 1: Write down factorisation of each number:

512 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2

320 = 2 · 2 · 2 · 2 · 2 · 2 · 5

Step 2 : Match primes vertically:

512=2·2·2·2·2·2·2·2·2  
320=2·2·2·2·2·2·      5

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

512=2·2·2·2·2·2·2·2·2    
320=2·2·2·2·2·2·      5  
LCM=2·2·2·2·2·2·2·2·2·5=2560

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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