Find Least Common Multiple of 45, 108, 144 and 180 using division method..

Answer

LCM( 45, 108, 144, 180 ) = 2160

Explanation

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

108

144

180

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	45	108	144	180
	45	54	72	90

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

2	45	108	144	180
2	45	54	72	90
2	45	27	36	45
2	45	27	18	45
3	45	27	9	45
3	15	9	3	15
3	5	3	1	5
5	5	1	1	5
	1	1	1	1

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

LCM( 45, 108, 144, 180 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 = 2160 .

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2	45	108	144	180
2	45	54	72	90
2	45	27	36	45
2	45	27	18	45
3	45	27	9	45
3	15	9	3	15
3	5	3	1	5
5	5	1	1	5
	1	1	1	1

2	45	108	144	180
2	45	54	72	90
2	45	27	36	45
2	45	27	18	45
3	45	27	9	45
3	15	9	3	15
3	5	3	1	5
5	5	1	1	5
	1	1	1	1

2	45	108	144	180
2	45	54	72	90
2	45	27	36	45
2	45	27	18	45
3	45	27	9	45
3	15	9	3	15
3	5	3	1	5
5	5	1	1	5
	1	1	1	1