Finite Math Examples

Find the LCM 13/(30x^2) , 13/(18x)
,
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
To find the LCM for a list of fractions, check if denominators are similar or not.
Fractions with the same denominator:
1:
Fractions with different denominators such as, :
1: Find the LCM of and
2: Multiply the numerator and denominator of the first fraction by
3: Multiply the numerator and denominator of the second fraction by
4: After making the denominators for all the fractions same, in this case, only two fractions, find the LCM of the new numerators
5: The LCM will be the
Step 3
Find the LCM for the denominators of .
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Step 3.1
Simplify each term.
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Step 3.1.1
Raise to the power of .
Step 3.1.2
Use the power rule to combine exponents.
Step 3.1.3
Add and .
Step 3.1.4
Raise to the power of .
Step 3.1.5
Use the power rule to combine exponents.
Step 3.1.6
Add and .
Step 3.2
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 3.3
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 3.4
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 3.5
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 3.6
The factors for are , which is multiplied by each other times.
occurs times.
Step 3.7
The factor for is itself.
occurs time.
Step 3.8
The factors for are , which is multiplied by each other times.
occurs times.
Step 3.9
The factor for is itself.
occurs time.
Step 3.10
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 3.11
Multiply by .
Step 4
Multiply each number by , where is a number that makes the denominator .
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Step 4.1
Multiply the numerator and denominator of by .
Step 4.2
Combine and .
Step 4.3
Cancel the common factor of .
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Step 4.3.1
Cancel the common factor.
Step 4.3.2
Rewrite the expression.
Step 4.4
Multiply the numerator and denominator of by .
Step 4.5
Cancel the common factor of .
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Step 4.5.1
Cancel the common factor.
Step 4.5.2
Rewrite the expression.
Step 4.6
Cancel the common factor of .
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Step 4.6.1
Cancel the common factor.
Step 4.6.2
Divide by .
Step 4.7
Multiply by .
Step 4.8
Cancel the common factor of .
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Step 4.8.1
Cancel the common factor.
Step 4.8.2
Rewrite the expression.
Step 4.9
Cancel the common factor of .
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Step 4.9.1
Cancel the common factor.
Step 4.9.2
Divide by .
Step 4.10
Multiply by .
Step 4.11
Write the new list with the same denominators.
Step 5
Find the LCM for .
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Step 5.1
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 5.2
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 5.3
Since has no factors besides and .
is a prime number
Step 5.4
has factors of and .
Step 5.5
Multiply by .
Step 5.6
The factors for are , which is multiplied by each other times.
occurs times.
Step 5.7
The factor for is itself.
occurs time.
Step 5.8
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 5.9
Multiply by .
Step 5.10
The LCM for is the numeric part multiplied by the variable part.
Step 6
The answer can be found by taking the LCM of and dividing by the LCM of .
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Step 6.1
Divide the LCM of by the LCM of .
Step 6.2
Cancel the common factor of .
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Step 6.2.1
Cancel the common factor.
Step 6.2.2
Rewrite the expression.
Step 6.3
Cancel the common factor of .
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Step 6.3.1
Cancel the common factor.
Step 6.3.2
Divide by .
Step 7
The factors for are , which is multiplied by each other times.
occurs times.
Step 8
The factor for is itself.
occurs time.
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
Multiply by .
Step 11
The LCM for is the numeric part multiplied by the variable part.