Find Least Common Multiple of 64, 96, 120 and 108 using division method..

Answer

LCM( 64, 96, 120, 108 ) = 8640

Explanation

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

120

108

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	64	96	120	108
	32	48	60	54

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

2	64	96	120	108
2	32	48	60	54
2	16	24	30	27
2	8	12	15	27
2	4	6	15	27
2	2	3	15	27
3	1	3	15	27
3	1	1	5	9
3	1	1	5	3
5	1	1	5	1
	1	1	1	1

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

LCM( 64, 96, 120, 108 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 = 8640 .

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2	64	96	120	108
2	32	48	60	54
2	16	24	30	27
2	8	12	15	27
2	4	6	15	27
2	2	3	15	27
3	1	3	15	27
3	1	1	5	9
3	1	1	5	3
5	1	1	5	1
	1	1	1	1

2	64	96	120	108
2	32	48	60	54
2	16	24	30	27
2	8	12	15	27
2	4	6	15	27
2	2	3	15	27
3	1	3	15	27
3	1	1	5	9
3	1	1	5	3
5	1	1	5	1
	1	1	1	1

2	64	96	120	108
2	32	48	60	54
2	16	24	30	27
2	8	12	15	27
2	4	6	15	27
2	2	3	15	27
3	1	3	15	27
3	1	1	5	9
3	1	1	5	3
5	1	1	5	1
	1	1	1	1