1. The problem is to find the Least Common Multiple (LCM) of given numbers using prime factorization. 2. Prime factorization means breaking down each number into its prime factors. 3. For example, to find the LCM of 12 and 18: - Prime factorize 12: $$12 = 2^2 \times 3^1$$ - Prime factorize 18: $$18 = 2^1 \times 3^2$$ 4. To find the LCM, take the highest power of each prime factor from both numbers: - For 2, the highest power is $$2^2$$ - For 3, the highest power is $$3^2$$ 5. Multiply these highest powers together: $$LCM = 2^2 \times 3^2 = 4 \times 9 = 36$$ 6. Therefore, the LCM of 12 and 18 is 36. 7. This method works for any set of numbers: prime factorize each, then multiply the highest powers of all primes found.