What is the least common multiple of 5a squared and 7a cubed?
that would be 35a^6
since the exponents 2 and 3 are relatively prime
and 5 and 7 are relatively prime.
on second thought, it would be 35a^3
since 5a^2 and 7a^3 both divide that, but no lower power of a
To find the least common multiple (LCM) of 5a squared and 7a cubed, we can break down each expression into their prime factors and then take the highest power of each prime factor.
Let's start with 5a squared:
- The prime factorization of 5a squared is 5 * a * a.
Next, let's break down 7a cubed:
- The prime factorization of 7a cubed is 7 * a * a * a.
To find the LCM, we need to choose the highest power of each prime factor:
- The highest power of 5 is 1.
- The highest power of 7 is 1.
- The highest power of "a" is 3.
Therefore, the LCM of 5a squared and 7a cubed is 5 * 7 * a * a * a, which simplifies to 35a cubed.