Practice Math Questions for Praxis—Least Common Multiples

Despite their name, least common multiple (or LCM) problems are very likely to show up on the Praxis Core exam. In the following practice questions, you start with the LCM and have to find one of its factors; then, you have to do some (ugh) extra math to find the LCM.

Practice questions

1. Twenty-four is the least common multiple of 8 and which of the following numbers?

   A. 12 B. 36 C. 4 D. 16 E. 2

2. What is half the square of the least common multiple of 14 and 21?

   A. 882 B. 98 C. 1,764 D. 220.5 E. 196

Answers and explanations

1. The correct answer is Choice (A).
   Twenty-four is a multiple of only Choices (A), (C), and (E). You can list the first few multiples of those choices and 8 to determine the answer to the question. Here are the multiples of 8 and Choice (A): Multiples of 8: 8, 16, 24 … Multiples of 12: 12, 24, … Without going any further, you can see that 24 is the least common multiple of 8 and 12, so Choice (A) is correct. In case you're curious, 8, not 24, is the least common multiple of 8 and Choices (C) and (E).
2. The correct answer is Choice (A).
   Add each number to itself multiple times to find its first few multiples: Multiples of 14: 14, 28, 42, 56, 60, 74, … Multiples of 21: 21, 42, … You can see that 42 is the least common multiple of 14 and 21. The square of 42 is 42², which is

   42 × 42

   or 1,764. That number divided by 2, or times 1/2, is 882.