the least common multiple lcm of two numbers is the smallest number that is a multiple of both which of the following represents the lcm of 14 and 21
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HESI A2

HESI A2 Math Practice Test 2022

1. The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. Which of the following represents the LCM of 14 and 21?

Correct answer: C

Rationale: Rationale: To find the least common multiple (LCM) of 14 and 21, we need to determine the smallest number that is a multiple of both 14 and 21. First, list the multiples of 14: 14, 28, 42, 56, 70, 84, ... Next, list the multiples of 21: 21, 42, 63, 84, ... The smallest number that appears in both lists is 42. Therefore, the LCM of 14 and 21 is 42.

2. A healthcare professional works in a military hospital from 1300 to 2000. What time of day does this healthcare professional work?

Correct answer: C

Rationale: The shift from 1300 (1:00 PM) to 2000 (8:00 PM) corresponds to early afternoon to bedtime. Therefore, the correct answer is C, as this healthcare professional works during the early afternoon to bedtime hours. Choices A, B, and D are incorrect because the work hours fall within the early afternoon to evening time frame, not early morning, lunchtime, or midnight to sunrise.

3. A car travels 240 miles in 4 hours. What is its speed in miles per hour?

Correct answer: B

Rationale: To calculate speed, divide the distance traveled by the time taken: 240 miles ÷ 4 hours = 60 mph. Therefore, the correct answer is B. Choice A (50 mph) is incorrect as it results from an incorrect calculation. Choice C (55 mph) and D (75 mph) are also incorrect because they are not the correct result of dividing 240 miles by 4 hours.

4. What is the perimeter of a garden bed with a side length of 8 meters?

Correct answer: B

Rationale: The correct answer is B: 24m. The perimeter of a square is found by adding up all its sides. In this case, since the garden bed has a side length of 8 meters, the perimeter would be 8m + 8m + 8m + 8m = 24m. Choices A, C, and D are incorrect because they do not correctly calculate the perimeter of a square with a side length of 8 meters.

5. If Gwen's favorite summer drink is 2 parts fruit juice to 3 parts seltzer and she starts with a gallon of fruit juice, how many quarts of seltzer will she need?

Correct answer: D

Rationale: To maintain the ratio of 2 parts fruit juice to 3 parts seltzer, for every 2 parts of fruit juice, Gwen will need 3 parts of seltzer. Since a gallon of fruit juice is equivalent to 4 quarts, she will need 3 quarts of seltzer for every 2 quarts of fruit juice. For 4 quarts of fruit juice, she will require 6 quarts of seltzer. Therefore, Gwen will need 6 quarts of seltzer to make the summer drink for her friends. Choice A (3 quarts) is incorrect because it does not account for the correct ratio. Choice B (4.5 quarts) is incorrect because it is not a whole number and does not align with the ratio provided. Choice C (5 quarts) is incorrect as it does not match the proportional ratio of fruit juice to seltzer required.

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