Pre-Algebra Examples

Find the LCM 30ab^3 , 20ab^3
,
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
The prime factors for are .
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Step 3.1
has factors of and .
Step 3.2
has factors of and .
Step 4
The prime factors for are .
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Step 4.1
has factors of and .
Step 4.2
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 6.3
Multiply by .
Step 7
The factor for is itself.
occurs time.
Step 8
The factors for are , which is multiplied by each other times.
occurs times.
Step 9
The factor for is itself.
occurs time.
Step 10
The factors for are , which is multiplied by each other times.
occurs times.
Step 11
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 12
Simplify .
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Step 12.1
Multiply by by adding the exponents.
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Step 12.1.1
Move .
Step 12.1.2
Multiply by .
Step 12.2
Multiply by by adding the exponents.
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Step 12.2.1
Move .
Step 12.2.2
Multiply by .
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Step 12.2.2.1
Raise to the power of .
Step 12.2.2.2
Use the power rule to combine exponents.
Step 12.2.3
Add and .
Step 13
The LCM for is the numeric part multiplied by the variable part.