Pregunta
Find the least common multiple.
Write your answer as a constant times a product of single variables raised to exponents.
Write your answer as a constant times a product of single variables raised to exponents.
Ask by Bond Perkins. in the United States
Jan 22,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The least common multiple is
.
Solución
To find the least common multiple (LCM) of the expressions
and
, we will follow these steps:
- Identify the coefficients: The coefficients are
and . - Find the LCM of the coefficients: The LCM of
and can be calculated by finding the smallest multiple that both numbers share. - Identify the variable parts: The variable parts are
and . - Find the LCM of the variable parts: The LCM of
and is determined by taking the variable with the highest exponent.
Now, let’s calculate the LCM step by step.
Step 1: LCM of the coefficients
The prime factorization of the coefficients:
The LCM is found by taking the highest power of each prime:
- For
: - For
: - For
:
Thus, the LCM of the coefficients is:
Step 2: LCM of the variable parts
The variable parts are
and
. The LCM is:
Final LCM
Combining both results, we have:
Thus, the least common multiple is:
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Como
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Extra Insights
To find the least common multiple (LCM) of
and
, we first identify the LCM of the coefficients and the LCM of the variable parts separately.
The coefficients are
and
. The LCM of
and
is
.
Now, for the variable part
and
, we take the highest exponent, which is
.
Combining these, the least common multiple is:
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