Find Least Common Multiple of 256, 684 and 965 using division method..

Answer

LCM( 256, 684, 965 ) = 42243840

Explanation

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

256

684

965

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	684	965
	128	342	965

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

2	256	684	965
2	128	342	965
2	64	171	965
2	32	171	965
2	16	171	965
2	8	171	965
2	4	171	965
2	2	171	965
3	1	171	965
3	1	57	965
5	1	19	965
19	1	19	193
193	1	1	193
	1	1	1

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

LCM( 256, 684, 965 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 19 · 193 = 42243840 .

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	256	684	965
2	128	342	965
2	64	171	965
2	32	171	965
2	16	171	965
2	8	171	965
2	4	171	965
2	2	171	965
3	1	171	965
3	1	57	965
5	1	19	965
19	1	19	193
193	1	1	193
	1	1	1

2	256	684	965
2	128	342	965
2	64	171	965
2	32	171	965
2	16	171	965
2	8	171	965
2	4	171	965
2	2	171	965
3	1	171	965
3	1	57	965
5	1	19	965
19	1	19	193
193	1	1	193
	1	1	1

2	256	684	965
2	128	342	965
2	64	171	965
2	32	171	965
2	16	171	965
2	8	171	965
2	4	171	965
2	2	171	965
3	1	171	965
3	1	57	965
5	1	19	965
19	1	19	193
193	1	1	193
	1	1	1