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Question

Find Least Common Multiple of 840, 320, 480, 360 and 540 using prime factorisation method.

Answer

LCM( 840, 320, 480, 360, 540 ) = 60480

Explanation

Step 1: Write down factorisation of each number:

840 = 2 · 2 · 2 · 3 · 5 · 7

320 = 2 · 2 · 2 · 2 · 2 · 2 · 5

480 = 2 · 2 · 2 · 2 · 2 · 3 · 5

360 = 2 · 2 · 2 · 3 · 3 · 5

540 = 2 · 2 · 3 · 3 · 3 · 5

Step 2 : Match primes vertically:

840=2·2·2·      3·    5·7
320=2·2·2·2·2·2·      5  
480=2·2·2·2·2·  3·    5  
360=2·2·2·      3·3·  5  
540=2·2·        3·3·3·5  

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

840=2·2·2·      3·    5·7  
320=2·2·2·2·2·2·      5    
480=2·2·2·2·2·  3·    5    
360=2·2·2·      3·3·  5    
540=2·2·        3·3·3·5    
LCM=2·2·2·2·2·2·3·3·3·5·7=60480
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