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Find Least Common Multiple of 74, 64 and 968 using prime factorisation method.

Answer

LCM( 74, 64, 968 ) = 286528

Explanation

Step 1: Write down factorisation of each number:

74 = 2 · 37

64 = 2 · 2 · 2 · 2 · 2 · 2

968 = 2 · 2 · 2 · 11 · 11

Step 2 : Match primes vertically:

74=2·              37
64=2·2·2·2·2·2      
968=2·2·2·      11·11  

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

74=2·              37  
64=2·2·2·2·2·2        
968=2·2·2·      11·11    
LCM=2·2·2·2·2·2·11·11·37=286528

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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