Find Least Common Multiple of 164, 284 and 360 using division method..

Answer

LCM( 164, 284, 360 ) = 1047960

Explanation

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

164

284

360

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	164	284	360
	82	142	180

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

2	164	284	360
2	82	142	180
2	41	71	90
3	41	71	45
3	41	71	15
5	41	71	5
41	41	71	1
71	1	71	1
	1	1	1

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

LCM( 164, 284, 360 ) = 2 · 2 · 2 · 3 · 3 · 5 · 41 · 71 = 1047960 .

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	164	284	360
2	82	142	180
2	41	71	90
3	41	71	45
3	41	71	15
5	41	71	5
41	41	71	1
71	1	71	1
	1	1	1

2	164	284	360
2	82	142	180
2	41	71	90
3	41	71	45
3	41	71	15
5	41	71	5
41	41	71	1
71	1	71	1
	1	1	1

2	164	284	360
2	82	142	180
2	41	71	90
3	41	71	45
3	41	71	15
5	41	71	5
41	41	71	1
71	1	71	1
	1	1	1