Find Least Common Multiple of 30, 48, 108 and 210 using division method..

Answer

LCM( 30, 48, 108, 210 ) = 15120

Explanation

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

108

210

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	30	48	108	210
	15	24	54	105

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

2	30	48	108	210
2	15	24	54	105
2	15	12	27	105
2	15	6	27	105
3	15	3	27	105
3	5	1	9	35
3	5	1	3	35
5	5	1	1	35
7	1	1	1	7
	1	1	1	1

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

LCM( 30, 48, 108, 210 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 7 = 15120 .

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2	30	48	108	210
2	15	24	54	105
2	15	12	27	105
2	15	6	27	105
3	15	3	27	105
3	5	1	9	35
3	5	1	3	35
5	5	1	1	35
7	1	1	1	7
	1	1	1	1

2	30	48	108	210
2	15	24	54	105
2	15	12	27	105
2	15	6	27	105
3	15	3	27	105
3	5	1	9	35
3	5	1	3	35
5	5	1	1	35
7	1	1	1	7
	1	1	1	1

2	30	48	108	210
2	15	24	54	105
2	15	12	27	105
2	15	6	27	105
3	15	3	27	105
3	5	1	9	35
3	5	1	3	35
5	5	1	1	35
7	1	1	1	7
	1	1	1	1