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Question

Find Least Common Multiple of 144, 240 and 320 using prime factorisation method.

Answer

LCM( 144, 240, 320 ) = 2880

Explanation

Step 1: Write down factorisation of each number:

144 = 2 · 2 · 2 · 2 · 3 · 3

240 = 2 · 2 · 2 · 2 · 3 · 5

320 = 2 · 2 · 2 · 2 · 2 · 2 · 5

Step 2 : Match primes vertically:

144=2·2·2·2·    3·3  
240=2·2·2·2·    3·  5
320=2·2·2·2·2·2·    5

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

144=2·2·2·2·    3·3    
240=2·2·2·2·    3·  5  
320=2·2·2·2·2·2·    5  
LCM=2·2·2·2·2·2·3·3·5=2880

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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