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Find Least Common Multiple of 16, 24 and 32 using prime factorisation method.

Answer

LCM( 16, 24, 32 ) = 96

Explanation

Step 1: Write down factorisation of each number:

16 = 2 · 2 · 2 · 2

24 = 2 · 2 · 2 · 3

32 = 2 · 2 · 2 · 2 · 2

Step 2 : Match primes vertically:

16=2·2·2·2    
24=2·2·2·    3
32=2·2·2·2·2  

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

16=2·2·2·2      
24=2·2·2·    3  
32=2·2·2·2·2    
LCM=2·2·2·2·2·3=96

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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