Find Least Common Multiple of 576, 720 and 864 using division method..

Answer

LCM( 576, 720, 864 ) = 8640

Explanation

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

576

720

864

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	576	720	864
	288	360	432

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

2	576	720	864
2	288	360	432
2	144	180	216
2	72	90	108
2	36	45	54
2	18	45	27
3	9	45	27
3	3	15	9
3	1	5	3
5	1	5	1
	1	1	1

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

LCM( 576, 720, 864 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 = 8640 .

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	576	720	864
2	288	360	432
2	144	180	216
2	72	90	108
2	36	45	54
2	18	45	27
3	9	45	27
3	3	15	9
3	1	5	3
5	1	5	1
	1	1	1

2	576	720	864
2	288	360	432
2	144	180	216
2	72	90	108
2	36	45	54
2	18	45	27
3	9	45	27
3	3	15	9
3	1	5	3
5	1	5	1
	1	1	1

2	576	720	864
2	288	360	432
2	144	180	216
2	72	90	108
2	36	45	54
2	18	45	27
3	9	45	27
3	3	15	9
3	1	5	3
5	1	5	1
	1	1	1