what is the least common multiple lcm of 4 and 6
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HESI A2

HESI A2 Quizlet Math

1. What is the least common multiple (LCM) of 4 and 6?

Correct answer: A

Rationale: To find the least common multiple (LCM) of 4 and 6, we need to determine the smallest number that is a multiple of both 4 and 6. The multiples of 4 are: 4, 8, 12, 16, 20, 24, ... The multiples of 6 are: 6, 12, 18, 24, ... The least common multiple is the smallest number that appears in both lists. In this case, the least common multiple of 4 and 6 is 12, not 24. Therefore, the correct answer is 24. Choice B (12) is actually the least common multiple of 4 and 3, not 4 and 6. Choices C (6) and D (3) are not multiples of both 4 and 6, so they are incorrect.

2. If a runner runs 5 miles in 45 minutes, what is their average speed in miles per hour?

Correct answer: A

Rationale: To find the average speed, first, convert 45 minutes to hours (45/60 = 0.75 hours). Then, divide the distance by the time: 5 miles ÷ 0.75 hours = 6.67 mph. Choice A is correct because it accurately calculates the average speed based on the distance covered and time taken. Choice B is incorrect as it does not consider the time taken to cover the distance. Choice C is incorrect as it is higher than the calculated speed. Choice D is incorrect as it is higher and does not match the calculated average speed.

3. What is the boiling point of water in degrees Fahrenheit?

Correct answer: C

Rationale: The correct answer is C: '212°F.' The boiling point of water at standard atmospheric pressure is 212°F. This is the temperature at which water transitions from a liquid to a gas phase, known as boiling. It is a fundamental property of water and a crucial point to remember for various applications in science and everyday life. Choice A (100°F) is the boiling point of water in degrees Celsius, not Fahrenheit. Choice B (200°F) and Choice D (250°F) are not correct boiling points for water at standard atmospheric pressure.

4. If 1 pound equals 453.59 grams, how many grams would a 7 lb. baby weigh?

Correct answer: A

Rationale: To convert pounds to grams, multiply the weight in pounds by the conversion factor of 453.59 grams per pound. Therefore, 7 pounds x 453.59 grams/pound = 3175.13 grams, which is the weight of a 7 lb. baby in grams. Choice A is correct. Choice B (4000 grams) is incorrect as it does not use the correct conversion factor. Choice C (4535 grams) is incorrect as it seems to have used a rounding error. Choice D (3500 grams) is incorrect as it does not apply the correct conversion factor.

5. The price of an item increased from $9.00 to $10.00. What percentage did the price increase by?

Correct answer: B

Rationale: To calculate the percentage increase, subtract the original price from the new price, then divide the result by the original price and multiply by 100. In this case, the increase is $10.00 - $9.00 = $1.00. $1.00 divided by $9.00 is approximately 0.1111, which equals 11.11%, making choice B the correct answer. Choice A, 5%, is too low as the increase is more than 5%. Choice C, 20%, and choice D, 25%, are too high, exaggerating the actual increase of $1.00.

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