Find Least Common Multiple of 324 and 512 using division method..

Answer

LCM( 324, 512 ) = 41472

Explanation

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

324

512

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	324	512
	162	256

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

2	324	512
2	162	256
2	81	128
2	81	64
2	81	32
2	81	16
2	81	8
2	81	4
2	81	2
3	81	1
3	27	1
3	9	1
3	3	1
	1	1

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

LCM( 324, 512 ) = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 3 = 41472 .

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	324	512
2	162	256
2	81	128
2	81	64
2	81	32
2	81	16
2	81	8
2	81	4
2	81	2
3	81	1
3	27	1
3	9	1
3	3	1
	1	1

2	324	512
2	162	256
2	81	128
2	81	64
2	81	32
2	81	16
2	81	8
2	81	4
2	81	2
3	81	1
3	27	1
3	9	1
3	3	1
	1	1

2	324	512
2	162	256
2	81	128
2	81	64
2	81	32
2	81	16
2	81	8
2	81	4
2	81	2
3	81	1
3	27	1
3	9	1
3	3	1
	1	1