Explanation:

- The least common multiple (LCM) of two numbers \(a\) and \(b\) is 42. This means both numbers are factors of 42.

- We will need to find the LCM of \(5a\) and \(11b\).

- The LCM of numbers is determined by the highest power of all prime factors present.

- Since \(a\) and \(b\) are factors of 42, \(a\) and \(b\) could include the prime factors 2, 3, and 7.

- Let's find the LCM of \(5a\) and \(11b\), which is \(5 \times 11 \times LCM(a, b) = 5 \times 11 \times 42 = 2310\).

- 2310 is the correct answer.

- Option 1: 2310 is indeed the correct choice.

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