Find Least Common Multiple of 105, 140 and 315 using division method..

LCM( 105, 140, 315 ) = 1260

Step 1 : Write the given numbers in a horizontal line.

Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.

(if any number is not divisible by 2, write it down unchanged)

Step 3 : Continue dividing by prime numbers till we get 1 in all columns.

Step 4 : Multiply numbers in first column to get LCM.

LCM( 105, 140, 315 ) = 2 · 2 · 3 · 3 · 5 · 7 = 1260 .

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.