Find Least Common Multiple of 32, 124 and 315 using division method..

Answer

LCM( 32, 124, 315 ) = 312480

Explanation

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

124

315

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	32	124	315
	16	62	315

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

2	32	124	315
2	16	62	315
2	8	31	315
2	4	31	315
2	2	31	315
3	1	31	315
3	1	31	105
5	1	31	35
7	1	31	7
31	1	31	1
	1	1	1

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

LCM( 32, 124, 315 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 7 · 31 = 312480 .

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	32	124	315
2	16	62	315
2	8	31	315
2	4	31	315
2	2	31	315
3	1	31	315
3	1	31	105
5	1	31	35
7	1	31	7
31	1	31	1
	1	1	1

2	32	124	315
2	16	62	315
2	8	31	315
2	4	31	315
2	2	31	315
3	1	31	315
3	1	31	105
5	1	31	35
7	1	31	7
31	1	31	1
	1	1	1

2	32	124	315
2	16	62	315
2	8	31	315
2	4	31	315
2	2	31	315
3	1	31	315
3	1	31	105
5	1	31	35
7	1	31	7
31	1	31	1
	1	1	1