Find Least Common Multiple of 320, 210 and 240 using division method..

Answer

LCM( 320, 210, 240 ) = 6720

Explanation

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

320

210

240

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)

2	320	210	240
	160	105	120

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

2	320	210	240
2	160	105	120
2	80	105	60
2	40	105	30
2	20	105	15
2	10	105	15
3	5	105	15
5	5	35	5
7	1	7	1
	1	1	1

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

LCM( 320, 210, 240 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 5 · 7 = 6720 .

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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2	320	210	240
2	160	105	120
2	80	105	60
2	40	105	30
2	20	105	15
2	10	105	15
3	5	105	15
5	5	35	5
7	1	7	1
	1	1	1

2	320	210	240
2	160	105	120
2	80	105	60
2	40	105	30
2	20	105	15
2	10	105	15
3	5	105	15
5	5	35	5
7	1	7	1
	1	1	1

2	320	210	240
2	160	105	120
2	80	105	60
2	40	105	30
2	20	105	15
2	10	105	15
3	5	105	15
5	5	35	5
7	1	7	1
	1	1	1