Find Least Common Multiple of 200, 256 and 356 using division method..

Answer

LCM( 200, 256, 356 ) = 569600

Explanation

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

200

256

356

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	200	256	356
	100	128	178

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

2	200	256	356
2	100	128	178
2	50	64	89
2	25	32	89
2	25	16	89
2	25	8	89
2	25	4	89
2	25	2	89
5	25	1	89
5	5	1	89
89	1	1	89
	1	1	1

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

LCM( 200, 256, 356 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 5 · 5 · 89 = 569600 .

This solution can be visualized using a Venn diagram.

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

This page was created using

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2	200	256	356
2	100	128	178
2	50	64	89
2	25	32	89
2	25	16	89
2	25	8	89
2	25	4	89
2	25	2	89
5	25	1	89
5	5	1	89
89	1	1	89
	1	1	1

2	200	256	356
2	100	128	178
2	50	64	89
2	25	32	89
2	25	16	89
2	25	8	89
2	25	4	89
2	25	2	89
5	25	1	89
5	5	1	89
89	1	1	89
	1	1	1

2	200	256	356
2	100	128	178
2	50	64	89
2	25	32	89
2	25	16	89
2	25	8	89
2	25	4	89
2	25	2	89
5	25	1	89
5	5	1	89
89	1	1	89
	1	1	1