Find Least Common Multiple of 640, 680 and 860 using division method..

Answer

LCM( 640, 680, 860 ) = 467840

Explanation

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

640

680

860

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	640	680	860
	320	340	430

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

2	640	680	860
2	320	340	430
2	160	170	215
2	80	85	215
2	40	85	215
2	20	85	215
2	10	85	215
5	5	85	215
17	1	17	43
43	1	1	43
	1	1	1

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

LCM( 640, 680, 860 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 5 · 17 · 43 = 467840 .

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	640	680	860
2	320	340	430
2	160	170	215
2	80	85	215
2	40	85	215
2	20	85	215
2	10	85	215
5	5	85	215
17	1	17	43
43	1	1	43
	1	1	1

2	640	680	860
2	320	340	430
2	160	170	215
2	80	85	215
2	40	85	215
2	20	85	215
2	10	85	215
5	5	85	215
17	1	17	43
43	1	1	43
	1	1	1

2	640	680	860
2	320	340	430
2	160	170	215
2	80	85	215
2	40	85	215
2	20	85	215
2	10	85	215
5	5	85	215
17	1	17	43
43	1	1	43
	1	1	1