Find Least Common Multiple of 360, 480 and 35 using division method..

Answer

LCM( 360, 480, 35 ) = 10080

Explanation

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

360

480

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	360	480	35
	180	240	35

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

2	360	480	35
2	180	240	35
2	90	120	35
2	45	60	35
2	45	30	35
3	45	15	35
3	15	5	35
5	5	5	35
7	1	1	7
	1	1	1

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

LCM( 360, 480, 35 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 7 = 10080 .

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	360	480	35
2	180	240	35
2	90	120	35
2	45	60	35
2	45	30	35
3	45	15	35
3	15	5	35
5	5	5	35
7	1	1	7
	1	1	1

2	360	480	35
2	180	240	35
2	90	120	35
2	45	60	35
2	45	30	35
3	45	15	35
3	15	5	35
5	5	5	35
7	1	1	7
	1	1	1

2	360	480	35
2	180	240	35
2	90	120	35
2	45	60	35
2	45	30	35
3	45	15	35
3	15	5	35
5	5	5	35
7	1	1	7
	1	1	1