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Question

Find Least Common Multiple of 160, 320 and 410 using prime factorisation method.

Answer

LCM( 160, 320, 410 ) = 13120

Explanation

Step 1: Write down factorisation of each number:

160 = 2 · 2 · 2 · 2 · 2 · 5

320 = 2 · 2 · 2 · 2 · 2 · 2 · 5

410 = 2 · 5 · 41

Step 2 : Match primes vertically:

160=2·2·2·2·2·  5  
320=2·2·2·2·2·2·5  
410=2·          5·41

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

160=2·2·2·2·2·  5    
320=2·2·2·2·2·2·5    
410=2·          5·41  
LCM=2·2·2·2·2·2·5·41=13120

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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