Find Least Common Multiple of 49, 99, 108 and 144 using division method..

Answer

LCM( 49, 99, 108, 144 ) = 232848

Explanation

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

108

144

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	49	99	108	144
	49	99	54	72

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

2	49	99	108	144
2	49	99	54	72
2	49	99	27	36
2	49	99	27	18
3	49	99	27	9
3	49	33	9	3
3	49	11	3	1
7	49	11	1	1
7	7	11	1	1
11	1	11	1	1
	1	1	1	1

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

LCM( 49, 99, 108, 144 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7 · 7 · 11 = 232848 .

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2	49	99	108	144
2	49	99	54	72
2	49	99	27	36
2	49	99	27	18
3	49	99	27	9
3	49	33	9	3
3	49	11	3	1
7	49	11	1	1
7	7	11	1	1
11	1	11	1	1
	1	1	1	1

2	49	99	108	144
2	49	99	54	72
2	49	99	27	36
2	49	99	27	18
3	49	99	27	9
3	49	33	9	3
3	49	11	3	1
7	49	11	1	1
7	7	11	1	1
11	1	11	1	1
	1	1	1	1

2	49	99	108	144
2	49	99	54	72
2	49	99	27	36
2	49	99	27	18
3	49	99	27	9
3	49	33	9	3
3	49	11	3	1
7	49	11	1	1
7	7	11	1	1
11	1	11	1	1
	1	1	1	1