Find Least Common Multiple of 256, 136 and 436 using division method..

Answer

LCM( 256, 136, 436 ) = 474368

Explanation

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

256

136

436

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	256	136	436
	128	68	218

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

2	256	136	436
2	128	68	218
2	64	34	109
2	32	17	109
2	16	17	109
2	8	17	109
2	4	17	109
2	2	17	109
17	1	17	109
109	1	1	109
	1	1	1

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

LCM( 256, 136, 436 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 17 · 109 = 474368 .

This solution can be visualized using a Venn diagram.

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

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2	256	136	436
2	128	68	218
2	64	34	109
2	32	17	109
2	16	17	109
2	8	17	109
2	4	17	109
2	2	17	109
17	1	17	109
109	1	1	109
	1	1	1

2	256	136	436
2	128	68	218
2	64	34	109
2	32	17	109
2	16	17	109
2	8	17	109
2	4	17	109
2	2	17	109
17	1	17	109
109	1	1	109
	1	1	1

2	256	136	436
2	128	68	218
2	64	34	109
2	32	17	109
2	16	17	109
2	8	17	109
2	4	17	109
2	2	17	109
17	1	17	109
109	1	1	109
	1	1	1