Find Least Common Multiple of 144, 176 and 256 using division method..

Answer

LCM( 144, 176, 256 ) = 25344

Explanation

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

144

176

256

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	144	176	256
	72	88	128

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

2	144	176	256
2	72	88	128
2	36	44	64
2	18	22	32
2	9	11	16
2	9	11	8
2	9	11	4
2	9	11	2
3	9	11	1
3	3	11	1
11	1	11	1
	1	1	1

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

LCM( 144, 176, 256 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 11 = 25344 .

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.

This page was created using

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2	144	176	256
2	72	88	128
2	36	44	64
2	18	22	32
2	9	11	16
2	9	11	8
2	9	11	4
2	9	11	2
3	9	11	1
3	3	11	1
11	1	11	1
	1	1	1

2	144	176	256
2	72	88	128
2	36	44	64
2	18	22	32
2	9	11	16
2	9	11	8
2	9	11	4
2	9	11	2
3	9	11	1
3	3	11	1
11	1	11	1
	1	1	1

2	144	176	256
2	72	88	128
2	36	44	64
2	18	22	32
2	9	11	16
2	9	11	8
2	9	11	4
2	9	11	2
3	9	11	1
3	3	11	1
11	1	11	1
	1	1	1