What is the product of the least common multiple and the greatest common factor of 22 and 48?
I write 22 and 48 as products of prime factors: 22 = 2 * 11 and 48 = 2^4 * 3. The LCM is the product of the highest power of each prime factor that appears in either factorization. So the LCM of 22 and 48 is 2^4 * 3 * 11 = 16 * 33 = 528. To find the GCF of 22 and 48, I can use the same prime factorizations. The GCF is the product of the lowest power of each prime factor that appears in both factorizations. So the GCF of 22 and 48 is 2 * 1 = 2. Now I have the LCM and the GCF, and I need to multiply them together. The product of the LCM and the GCF of 22 and 48 is 528 * 2 = 1056. 