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Find Least Common Multiple of 240, 360, 480 and 540 using prime factorisation method.

Answer

LCM( 240, 360, 480, 540 ) = 4320

Explanation

Step 1: Write down factorisation of each number:

240 = 2 · 2 · 2 · 2 · 3 · 5

360 = 2 · 2 · 2 · 3 · 3 · 5

480 = 2 · 2 · 2 · 2 · 2 · 3 · 5

540 = 2 · 2 · 3 · 3 · 3 · 5

Step 2 : Match primes vertically:

240=2·2·2·2·  3·    5
360=2·2·2·    3·3·  5
480=2·2·2·2·2·3·    5
540=2·2·      3·3·3·5

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

240=2·2·2·2·  3·    5  
360=2·2·2·    3·3·  5  
480=2·2·2·2·2·3·    5  
540=2·2·      3·3·3·5  
LCM=2·2·2·2·2·3·3·3·5=4320
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