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Question

Find Least Common Multiple of 480, 620, 780 and 850 using prime factorisation method.

Answer

LCM( 480, 620, 780, 850 ) = 16442400

Explanation

Step 1: Write down factorisation of each number:

480 = 2 · 2 · 2 · 2 · 2 · 3 · 5

620 = 2 · 2 · 5 · 31

780 = 2 · 2 · 3 · 5 · 13

850 = 2 · 5 · 5 · 17

Step 2 : Match primes vertically:

480=2·2·2·2·2·3·5        
620=2·2·        5·      31
780=2·2·      3·5·  13    
850=2·          5·5·  17  

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

480=2·2·2·2·2·3·5          
620=2·2·        5·      31  
780=2·2·      3·5·  13      
850=2·          5·5·  17    
LCM=2·2·2·2·2·3·5·5·13·17·31=16442400
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