Find Least Common Multiple of 52, 78, 108 and 117 using division method..

Answer

LCM( 52, 78, 108, 117 ) = 1404

Explanation

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

108

117

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	52	78	108	117
	26	39	54	117

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

2	52	78	108	117
2	26	39	54	117
3	13	39	27	117
3	13	13	9	39
3	13	13	3	13
13	13	13	1	13
	1	1	1	1

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

LCM( 52, 78, 108, 117 ) = 2 · 2 · 3 · 3 · 3 · 13 = 1404 .

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2	52	78	108	117
2	26	39	54	117
3	13	39	27	117
3	13	13	9	39
3	13	13	3	13
13	13	13	1	13
	1	1	1	1

2	52	78	108	117
2	26	39	54	117
3	13	39	27	117
3	13	13	9	39
3	13	13	3	13
13	13	13	1	13
	1	1	1	1

2	52	78	108	117
2	26	39	54	117
3	13	39	27	117
3	13	13	9	39
3	13	13	3	13
13	13	13	1	13
	1	1	1	1