To find the LCM (Least Common Multiple) of 70x³z and 45y⁴z², we need to factor each expression into its prime factors:
70x³z = 2 * 5 * 7 * x * x * x * z
45y⁴z² = 3 * 3 * 5 * y * y * y * y * z * z
Then, the LCM is the product of the highest powers of all the primes involved. Specifically, we need to include all the primes that appear in either factorization and take the highest power of each.
So, the LCM of 70x³z and 45y⁴z² is:
LCM = 2 * 3 * 3 * 5 * 7 * x³ * y⁴ * z²
LCM = 2 * 3² * 5 * 7 * x³ * y⁴ * z²
LCM = 1890x³y⁴z²
Therefore, the LCM of 70x³z and 45y⁴z² is 1890x³y⁴z².