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Algebra Examples
160160 , 900900 , 10501050
Step 1
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 2
Step 2.1
160160 has factors of 22 and 8080.
2⋅802⋅80
Step 2.2
8080 has factors of 22 and 4040.
2⋅2⋅402⋅2⋅40
Step 2.3
4040 has factors of 22 and 2020.
2⋅2⋅2⋅202⋅2⋅2⋅20
Step 2.4
2020 has factors of 22 and 1010.
2⋅2⋅2⋅2⋅102⋅2⋅2⋅2⋅10
Step 2.5
1010 has factors of 22 and 55.
2⋅2⋅2⋅2⋅2⋅52⋅2⋅2⋅2⋅2⋅5
2⋅2⋅2⋅2⋅2⋅52⋅2⋅2⋅2⋅2⋅5
Step 3
Step 3.1
900900 has factors of 22 and 450450.
2⋅4502⋅450
Step 3.2
450450 has factors of 22 and 225225.
2⋅2⋅2252⋅2⋅225
Step 3.3
225225 has factors of 33 and 7575.
2⋅2⋅3⋅752⋅2⋅3⋅75
Step 3.4
7575 has factors of 33 and 2525.
2⋅2⋅3⋅3⋅252⋅2⋅3⋅3⋅25
Step 3.5
2525 has factors of 55 and 55.
2⋅2⋅3⋅3⋅5⋅52⋅2⋅3⋅3⋅5⋅5
2⋅2⋅3⋅3⋅5⋅52⋅2⋅3⋅3⋅5⋅5
Step 4
Step 4.1
10501050 has factors of 22 and 525525.
2⋅5252⋅525
Step 4.2
525525 has factors of 33 and 175175.
2⋅3⋅1752⋅3⋅175
Step 4.3
175175 has factors of 55 and 3535.
2⋅3⋅5⋅352⋅3⋅5⋅35
Step 4.4
3535 has factors of 55 and 77.
2⋅3⋅5⋅5⋅72⋅3⋅5⋅5⋅7
2⋅3⋅5⋅5⋅72⋅3⋅5⋅5⋅7
Step 5
The LCM of 160,900,1050160,900,1050 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅72⋅2⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅7
Step 6
Step 6.1
Multiply 22 by 22.
4⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅74⋅2⋅2⋅2⋅3⋅3⋅5⋅5⋅7
Step 6.2
Multiply 44 by 22.
8⋅2⋅2⋅3⋅3⋅5⋅5⋅78⋅2⋅2⋅3⋅3⋅5⋅5⋅7
Step 6.3
Multiply 88 by 22.
16⋅2⋅3⋅3⋅5⋅5⋅716⋅2⋅3⋅3⋅5⋅5⋅7
Step 6.4
Multiply 1616 by 22.
32⋅3⋅3⋅5⋅5⋅732⋅3⋅3⋅5⋅5⋅7
Step 6.5
Multiply 3232 by 33.
96⋅3⋅5⋅5⋅796⋅3⋅5⋅5⋅7
Step 6.6
Multiply 9696 by 33.
288⋅5⋅5⋅7288⋅5⋅5⋅7
Step 6.7
Multiply 288288 by 55.
1440⋅5⋅71440⋅5⋅7
Step 6.8
Multiply 14401440 by 55.
7200⋅77200⋅7
Step 6.9
Multiply 72007200 by 77.
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