Find Least Common Multiple of 384, 320 and 420 using division method..

Answer

LCM( 384, 320, 420 ) = 13440

Explanation

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

384

320

420

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	384	320	420
	192	160	210

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

2	384	320	420
2	192	160	210
2	96	80	105
2	48	40	105
2	24	20	105
2	12	10	105
2	6	5	105
3	3	5	105
5	1	5	35
7	1	1	7
	1	1	1

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

LCM( 384, 320, 420 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 5 · 7 = 13440 .

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	384	320	420
2	192	160	210
2	96	80	105
2	48	40	105
2	24	20	105
2	12	10	105
2	6	5	105
3	3	5	105
5	1	5	35
7	1	1	7
	1	1	1

2	384	320	420
2	192	160	210
2	96	80	105
2	48	40	105
2	24	20	105
2	12	10	105
2	6	5	105
3	3	5	105
5	1	5	35
7	1	1	7
	1	1	1

2	384	320	420
2	192	160	210
2	96	80	105
2	48	40	105
2	24	20	105
2	12	10	105
2	6	5	105
3	3	5	105
5	1	5	35
7	1	1	7
	1	1	1