Answer :
To find the least common multiple (LCM) of the expressions [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex], follow these steps:
1. Identify the Coefficients:
- The coefficient of [tex]\(9x^4\)[/tex] is 9.
- The coefficient of [tex]\(6a^2\)[/tex] is 6.
2. Find the LCM of the Coefficients:
- The LCM of 9 and 6 is calculated by finding the smallest number that both 9 and 6 divide without a remainder. The LCM of 9 and 6 is 18.
3. Identify the Variables and their Exponents:
- In [tex]\(9x^4\)[/tex], the variable is [tex]\(x\)[/tex] with an exponent of 4.
- In [tex]\(6a^2\)[/tex], the variable is [tex]\(a\)[/tex] with an exponent of 2.
4. Determine the LCM for the Variables:
- For variable [tex]\(x\)[/tex], the highest exponent present is [tex]\(x^4\)[/tex] (since there is no [tex]\(x\)[/tex] in [tex]\(6a^2\)[/tex]).
- For variable [tex]\(a\)[/tex], the highest exponent present is [tex]\(a^2\)[/tex].
5. Combine the LCM of Coefficients and Variables:
- Combine the LCM of the coefficients (18) with the variables and their highest exponents: [tex]\(x^4\)[/tex] and [tex]\(a^2\)[/tex].
So, the least common multiple of [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex] is [tex]\(18x^4a^2\)[/tex].
1. Identify the Coefficients:
- The coefficient of [tex]\(9x^4\)[/tex] is 9.
- The coefficient of [tex]\(6a^2\)[/tex] is 6.
2. Find the LCM of the Coefficients:
- The LCM of 9 and 6 is calculated by finding the smallest number that both 9 and 6 divide without a remainder. The LCM of 9 and 6 is 18.
3. Identify the Variables and their Exponents:
- In [tex]\(9x^4\)[/tex], the variable is [tex]\(x\)[/tex] with an exponent of 4.
- In [tex]\(6a^2\)[/tex], the variable is [tex]\(a\)[/tex] with an exponent of 2.
4. Determine the LCM for the Variables:
- For variable [tex]\(x\)[/tex], the highest exponent present is [tex]\(x^4\)[/tex] (since there is no [tex]\(x\)[/tex] in [tex]\(6a^2\)[/tex]).
- For variable [tex]\(a\)[/tex], the highest exponent present is [tex]\(a^2\)[/tex].
5. Combine the LCM of Coefficients and Variables:
- Combine the LCM of the coefficients (18) with the variables and their highest exponents: [tex]\(x^4\)[/tex] and [tex]\(a^2\)[/tex].
So, the least common multiple of [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex] is [tex]\(18x^4a^2\)[/tex].
