Final answer:
To find the LCM of two numbers with prime factorizations 2² * 3 * 5 and 2 * 3² * 7, take the highest power of each prime from both factorizations to get 2² * 3² * 5 * 7, which simplifies to 1260.
Step-by-step explanation:
To find the least common multiple (LCM) of two numbers with given prime factorizations, we use each prime number with the highest power that appears in either factorization. The two numbers have prime factorizations of 2² * 3 * 5 and 2 * 3² * 7. To determine the LCM, we take the highest power of each prime number from the given factorizations.
For the prime number 2, the highest power in either factorization is 2² (from the first number). For the prime number 3, it's 3² (from the second number). The prime numbers 5 and 7 only appear in one factorization each, so we take 5¹ and 7¹ respectively. Therefore, the LCM is 2² * 3² * 5 * 7, which can also be written as 4 * 9 * 5 * 7, or simply 1260. This is the smallest number that is divisible by both original numbers.