Finite Math Examples

Find the LCM 10m^3 , 4w^4
,
Step 1
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 2
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 3
has factors of and .
Step 4
has factors of and .
Step 5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 6
Multiply .
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Step 6.1
Multiply by .
Step 6.2
Multiply by .
Step 7
The factors for are , which is multiplied by each other times.
occurs times.
Step 8
The factors for are , which is multiplied by each other times.
occurs times.
Step 9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 10
Simplify .
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Step 10.1
Multiply by .
Step 10.2
Multiply by by adding the exponents.
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Step 10.2.1
Multiply by .
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Step 10.2.1.1
Raise to the power of .
Step 10.2.1.2
Use the power rule to combine exponents.
Step 10.2.2
Add and .
Step 10.3
Multiply by by adding the exponents.
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Step 10.3.1
Move .
Step 10.3.2
Multiply by .
Step 10.4
Multiply by by adding the exponents.
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Step 10.4.1
Move .
Step 10.4.2
Multiply by .
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Step 10.4.2.1
Raise to the power of .
Step 10.4.2.2
Use the power rule to combine exponents.
Step 10.4.3
Add and .
Step 10.5
Multiply by by adding the exponents.
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Step 10.5.1
Move .
Step 10.5.2
Multiply by .
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Step 10.5.2.1
Raise to the power of .
Step 10.5.2.2
Use the power rule to combine exponents.
Step 10.5.3
Add and .
Step 11
The LCM for is the numeric part multiplied by the variable part.