Find Least Common Multiple of 400, 456 and 356 using division method..

Answer

LCM( 400, 456, 356 ) = 2029200

Explanation

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

400

456

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	400	456	356
	200	228	178

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

2	400	456	356
2	200	228	178
2	100	114	89
2	50	57	89
3	25	57	89
5	25	19	89
5	5	19	89
19	1	19	89
89	1	1	89
	1	1	1

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

LCM( 400, 456, 356 ) = 2 · 2 · 2 · 2 · 3 · 5 · 5 · 19 · 89 = 2029200 .

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	400	456	356
2	200	228	178
2	100	114	89
2	50	57	89
3	25	57	89
5	25	19	89
5	5	19	89
19	1	19	89
89	1	1	89
	1	1	1

2	400	456	356
2	200	228	178
2	100	114	89
2	50	57	89
3	25	57	89
5	25	19	89
5	5	19	89
19	1	19	89
89	1	1	89
	1	1	1

2	400	456	356
2	200	228	178
2	100	114	89
2	50	57	89
3	25	57	89
5	25	19	89
5	5	19	89
19	1	19	89
89	1	1	89
	1	1	1