Find Least Common Multiple of 91, 45 and 96 using division method..

Answer

LCM( 91, 45, 96 ) = 131040

Explanation

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

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	91	45	96
	91	45	48

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

2	91	45	96
2	91	45	48
2	91	45	24
2	91	45	12
2	91	45	6
3	91	45	3
3	91	15	1
5	91	5	1
7	91	1	1
13	13	1	1
	1	1	1

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

LCM( 91, 45, 96 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 7 · 13 = 131040 .

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	91	45	96
2	91	45	48
2	91	45	24
2	91	45	12
2	91	45	6
3	91	45	3
3	91	15	1
5	91	5	1
7	91	1	1
13	13	1	1
	1	1	1

2	91	45	96
2	91	45	48
2	91	45	24
2	91	45	12
2	91	45	6
3	91	45	3
3	91	15	1
5	91	5	1
7	91	1	1
13	13	1	1
	1	1	1

2	91	45	96
2	91	45	48
2	91	45	24
2	91	45	12
2	91	45	6
3	91	45	3
3	91	15	1
5	91	5	1
7	91	1	1
13	13	1	1
	1	1	1