Find Least Common Multiple of 460, 520, 640 and 688 using division method..

Answer

LCM( 460, 520, 640, 688 ) = 8228480

Explanation

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

460

520

640

688

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	520	640	688
	230	260	320	344

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

2	460	520	640	688
2	230	260	320	344
2	115	130	160	172
2	115	65	80	86
2	115	65	40	43
2	115	65	20	43
2	115	65	10	43
5	115	65	5	43
13	23	13	1	43
23	23	1	1	43
43	1	1	1	43
	1	1	1	1

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

LCM( 460, 520, 640, 688 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 5 · 13 · 23 · 43 = 8228480 .

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2	460	520	640	688
2	230	260	320	344
2	115	130	160	172
2	115	65	80	86
2	115	65	40	43
2	115	65	20	43
2	115	65	10	43
5	115	65	5	43
13	23	13	1	43
23	23	1	1	43
43	1	1	1	43
	1	1	1	1

2	460	520	640	688
2	230	260	320	344
2	115	130	160	172
2	115	65	80	86
2	115	65	40	43
2	115	65	20	43
2	115	65	10	43
5	115	65	5	43
13	23	13	1	43
23	23	1	1	43
43	1	1	1	43
	1	1	1	1

2	460	520	640	688
2	230	260	320	344
2	115	130	160	172
2	115	65	80	86
2	115	65	40	43
2	115	65	20	43
2	115	65	10	43
5	115	65	5	43
13	23	13	1	43
23	23	1	1	43
43	1	1	1	43
	1	1	1	1