Final answer:
To find the LCM of 49 and 98, we use prime factorization. Both numbers factor into primes with a base of 7, and the largest, 98, is already the LCM, since both 49 and 98 are multiples of 7.
Step-by-step explanation:
The least common multiple (LCM) is the smallest number that is a multiple of both numbers in a given pair. To find the LCM of 49 and 98 using prime factorization, we first break each number down into its prime factors. The number 49 is 7×7 and 98 is 7×2×7. The LCM is then determined by taking the highest power of each prime that appears in the factorization of either number. Since the highest power of 7 in 98 is 7×2 (since 98 is composed of 7×2×7), and there is no need to repeat the prime number 7, the LCM of 49 and 98 is the same as the largest number, which is 98 itself.