Answer :
To find the least common multiple (LCM) of the expressions [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex], let's break down the steps:
1. Understand the Terms:
- The expression [tex]\(9x^4\)[/tex] consists of the coefficient 9 and the variable term [tex]\(x^4\)[/tex].
- The expression [tex]\(6a^2\)[/tex] consists of the coefficient 6 and the variable term [tex]\(a^2\)[/tex].
2. Find the LCM of the Coefficients:
- The coefficients are 9 and 6.
- To find the LCM of these numbers, list their prime factorizations:
- [tex]\(9 = 3 \times 3\)[/tex]
- [tex]\(6 = 2 \times 3\)[/tex]
- The LCM is found by taking the highest power of all prime numbers present in the factorizations:
- For 2, the highest power is [tex]\(2^1\)[/tex].
- For 3, the highest power is [tex]\(3^2\)[/tex].
- Therefore, the LCM of 9 and 6 is [tex]\(2^1 \times 3^2 = 18\)[/tex].
3. Combine the Variables:
- The variable parts are [tex]\(x^4\)[/tex] and [tex]\(a^2\)[/tex].
- For finding the LCM of variables, simply take both since they involve different variable bases:
- [tex]\(x^4\)[/tex] does not overlap with [tex]\(a^2\)[/tex], so both are included in the LCM.
4. Form the LCM Expression:
- Combine the LCM of the coefficients with the variables:
- The LCM of the entire expressions is [tex]\(18 \times x^4 \times a^2\)[/tex].
Thus, the least common multiple of [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex] is [tex]\(18a^2x^4\)[/tex].
1. Understand the Terms:
- The expression [tex]\(9x^4\)[/tex] consists of the coefficient 9 and the variable term [tex]\(x^4\)[/tex].
- The expression [tex]\(6a^2\)[/tex] consists of the coefficient 6 and the variable term [tex]\(a^2\)[/tex].
2. Find the LCM of the Coefficients:
- The coefficients are 9 and 6.
- To find the LCM of these numbers, list their prime factorizations:
- [tex]\(9 = 3 \times 3\)[/tex]
- [tex]\(6 = 2 \times 3\)[/tex]
- The LCM is found by taking the highest power of all prime numbers present in the factorizations:
- For 2, the highest power is [tex]\(2^1\)[/tex].
- For 3, the highest power is [tex]\(3^2\)[/tex].
- Therefore, the LCM of 9 and 6 is [tex]\(2^1 \times 3^2 = 18\)[/tex].
3. Combine the Variables:
- The variable parts are [tex]\(x^4\)[/tex] and [tex]\(a^2\)[/tex].
- For finding the LCM of variables, simply take both since they involve different variable bases:
- [tex]\(x^4\)[/tex] does not overlap with [tex]\(a^2\)[/tex], so both are included in the LCM.
4. Form the LCM Expression:
- Combine the LCM of the coefficients with the variables:
- The LCM of the entire expressions is [tex]\(18 \times x^4 \times a^2\)[/tex].
Thus, the least common multiple of [tex]\(9x^4\)[/tex] and [tex]\(6a^2\)[/tex] is [tex]\(18a^2x^4\)[/tex].
