Final Answer:
The least common multiple (LCM) of 49 and 42 is 294.
Step-by-step explanation:
To find the LCM of 49 and 42, we need to identify the prime factors of each number and then take the highest power of each prime factor. The prime factorization of 49 is 7<sup>2</sup>, and the prime factorization of 42 is 2<sup>1</sup> * 3<sup>1</sup> * 7<sup>1</sup>. To find the LCM, we take the highest powers of each prime factor, which gives us 2<sup>1</sup> * 3<sup>1</sup> * 7<sup>2</sup>, resulting in the LCM of 294.
In summary, the LCM is the smallest multiple that both numbers share. By breaking down each number into its prime factors and selecting the highest powers, we determine the LCM. In this case, the LCM of 49 and 42 is 294, representing the smallest common multiple that satisfies both numbers. This process ensures an accurate and efficient way to calculate the least common multiple of two given integers.