Find Least Common Multiple of 96, 64, 108 and 72 using division method..

Answer

LCM( 96, 64, 108, 72 ) = 1728

Explanation

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

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	96	64	108	72
	48	32	54	36

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

2	96	64	108	72
2	48	32	54	36
2	24	16	27	18
2	12	8	27	9
2	6	4	27	9
2	3	2	27	9
3	3	1	27	9
3	1	1	9	3
3	1	1	3	1
	1	1	1	1

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

LCM( 96, 64, 108, 72 ) = 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 = 1728 .

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2	96	64	108	72
2	48	32	54	36
2	24	16	27	18
2	12	8	27	9
2	6	4	27	9
2	3	2	27	9
3	3	1	27	9
3	1	1	9	3
3	1	1	3	1
	1	1	1	1

2	96	64	108	72
2	48	32	54	36
2	24	16	27	18
2	12	8	27	9
2	6	4	27	9
2	3	2	27	9
3	3	1	27	9
3	1	1	9	3
3	1	1	3	1
	1	1	1	1

2	96	64	108	72
2	48	32	54	36
2	24	16	27	18
2	12	8	27	9
2	6	4	27	9
2	3	2	27	9
3	3	1	27	9
3	1	1	9	3
3	1	1	3	1
	1	1	1	1