Find Least Common Multiple of 460, 684, 764 and 400 using division method..

Answer

LCM( 460, 684, 764, 400 ) = 300481200

Explanation

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

460

684

764

400

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	460	684	764	400
	230	342	382	200

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

2	460	684	764	400
2	230	342	382	200
2	115	171	191	100
2	115	171	191	50
3	115	171	191	25
3	115	57	191	25
5	115	19	191	25
5	23	19	191	5
19	23	19	191	1
23	23	1	191	1
191	1	1	191	1
	1	1	1	1

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

LCM( 460, 684, 764, 400 ) = 2 · 2 · 2 · 2 · 3 · 3 · 5 · 5 · 19 · 23 · 191 = 300481200 .

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2	460	684	764	400
2	230	342	382	200
2	115	171	191	100
2	115	171	191	50
3	115	171	191	25
3	115	57	191	25
5	115	19	191	25
5	23	19	191	5
19	23	19	191	1
23	23	1	191	1
191	1	1	191	1
	1	1	1	1

2	460	684	764	400
2	230	342	382	200
2	115	171	191	100
2	115	171	191	50
3	115	171	191	25
3	115	57	191	25
5	115	19	191	25
5	23	19	191	5
19	23	19	191	1
23	23	1	191	1
191	1	1	191	1
	1	1	1	1

2	460	684	764	400
2	230	342	382	200
2	115	171	191	100
2	115	171	191	50
3	115	171	191	25
3	115	57	191	25
5	115	19	191	25
5	23	19	191	5
19	23	19	191	1
23	23	1	191	1
191	1	1	191	1
	1	1	1	1