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Find the LCM of the following. Leave the answers as prime factors.
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5 partsStep-by-step solution
15 stepsTo find the Least Common Multiple (LCM) of numbers expressed in prime factor form, we first express each number in index notation. Then, we identify all unique prime factors present in any of the numbers and take the highest power for each of those unique prime factors. Finally, we multiply these highest powers together.
Part a· 3 steps
The given numbers are: ; ;
Express each number in index notation.
Identify all unique prime factors and their highest powers.
Unique prime factors are 2, 3, and 5.
Highest power of 2: (from and )
Highest power of 3: (from )
Highest power of 5: (from and )Multiply the highest powers of the unique prime factors.
The LCM for part a is .
Part b
The given numbers are: ; ;
Express each number in index notation.
Identify all unique prime factors and their highest powers.
Unique prime factors are 2, 3, and 5.
Highest power of 2: (from )
Highest power of 3: (from )
Highest power of 5: (from )Multiply the highest powers of the unique prime factors.
The LCM for part b is .
Part c
The given numbers are: ; ;
Express each number in index notation.
Identify all unique prime factors and their highest powers.
Unique prime factors are 2, 3, and 5.
Highest power of 2: (from )
Highest power of 3: (from )
Highest power of 5: (from )Multiply the highest powers of the unique prime factors.
The LCM for part c is .
Part d
The given numbers are: ; ; ;
Express each number in index notation.
Identify all unique prime factors and their highest powers.
Unique prime factors are 2, 3, 5, and 7.
Highest power of 2: (from and )
Highest power of 3: (from )
Highest power of 5: (from )
Highest power of 7: (from , , and )Multiply the highest powers of the unique prime factors.
The LCM for part d is .
Part e
The given numbers are: ; ; ;
Express each number in index notation.
Identify all unique prime factors and their highest powers.
Unique prime factors are 2, 3, 5, and 7.
Highest power of 2: (from and )
Highest power of 3: (from )
Highest power of 5: (from )
Highest power of 7: (from and )Multiply the highest powers of the unique prime factors.
The LCM for part e is .
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