Question

What is the least common multiple of 2x³,5x⁴, and 8x⁶?

Answer 1

The least common multiple of 2x³, 5x⁴, and 8x⁶ is 8x⁶.

Step-by-step explanation:

To find the least common multiple (LCM) of 2x³, 5x⁴, and 8x⁶, we need to determine the highest power of each variable that appears in any of the given expressions. In this case, the highest power of x is 6, so we can rewrite each expression to have an exponent of 6.

2x³ = (2x³)(x³) = 2x⁶

5x⁴ = (5x⁴)(x²) = 5x⁶

8x⁶ = 8x⁶ (already in the desired form)

Now, we can see that the LCM of 2x³, 5x⁴, and 8x⁶ is 8x⁶.

Answer 2

The least common multiple (LCM) of 2x³, 5x⁴, and 8x⁶ is 40x⁶.

Step-by-step explanation:

To find the least common multiple (LCM) of the given algebraic expressions 2x³, 5x⁴, and 8x⁶, we need to identify the highest powers of each unique factor. The LCM is formed by taking the maximum exponent for each factor.

For the factor 2, the highest power is 8 (from 2x⁶). For the factor x, the highest power is x⁶. Therefore, the LCM is 8x⁶. Multiplying the coefficients, 2, 5, and 8, gives us the final result: 40x⁶.

The LCM ensures that each expression is a factor of the resulting expression, making it the smallest expression in which all the given expressions divide evenly. In this case, 2x³, 5x⁴, and 8x⁶ all divide evenly into 40x⁶. This property is particularly useful in simplifying expressions and solving equations involving multiple terms with different powers. The calculation of LCM is essential in various mathematical applications, ensuring a systematic approach to handling algebraic expressions and equations.