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Questions and Answers
What does a person need to find in order to determine the maximum number of identical refreshment tables they can stock for an American football game?
In a scenario where six bells toll together every two minutes, what mathematical concept is being applied to determine this interval?
How do real-life scenarios often demonstrate the importance of HCF and LCM concepts?
What would be the outcome of finding the LCM of the neon light blinking intervals to solve a problem involving their synchronization?
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When faced with a word problem involving both LCM and HCF, what mathematical skills are required from a student to successfully solve it?
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How many times will the traffic lights mentioned in the text change together in 30 minutes?
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If two students start blinking at the same time, one every 4 seconds and the other every 6 seconds, how many times will they blink together in 2 minutes?
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In a scenario where pencils cost $2 each and erasers cost $3 each, what is the least amount a student can spend to buy an equal number of pencils and erasers?
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Considering two pencils costing $4 each and three erasers costing $3 each, how many packages should a student buy to have an equal number of pencils and erasers without leftovers?
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If a set of traffic lights change every 15, 24, and 30 seconds respectively, how many times will they collectively change in 10 minutes?
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Study Notes
Word Problems Based on LCM and HCF
Interpreting Word Problems to Identify LCM and HCF
Word problems based on the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) require students to interpret the problem, determine the relevant information, and apply their knowledge of HCF and LCM to find the answer. For example, a word problem may ask how many times six bells toll together every minute. In this case, the problem requires the student to recognize that the LCM of the tolling intervals (2, 4, 6, 8, 10, and 12) is 120 seconds, or 2 minutes. By finding the LCM, the student can determine that the bells toll together every two minutes.
Applying LCM and HCF in Real-Life Scenarios
Real-life scenarios often involve situations where HCF and LCM are important concepts. For example, a person may want to create identical refreshment tables for an American football game and has a certain number of cans of regular soda and diet soda. By finding the greatest common factor between the number of cans of each type, the person can determine the maximum number of identical refreshment tables they can stock.
Solving Word Problems Involving Both LCM and HCF
Solving word problems involving both LCM and HCF requires a combination of understanding the problem, identifying the relevant information, and applying the appropriate mathematical concepts. For example, a problem may ask how many times two neon lights blink at the same time in a certain period. In this case, the student would need to find the LCM of the blinking intervals (4 and 6 seconds) and then divide the total time by this LCM to find the number of times they blink at the same time.
Finding the HCF in Word Problems
Finding the HCF in a word problem often involves identifying the greatest common divisor between two or more numbers. For example, a problem may ask how many times two pencils and two erasers can be purchased without any remaining. In this case, the student would need to find the HCF of the prices of the pencils and erasers to determine the least number of packages to buy.
Finding the LCM in Word Problems
Finding the LCM in a word problem involves identifying the smallest common multiple of two or more numbers. For example, a problem may ask how many times three different traffic lights change together every minute. In this case, the student would need to find the LCM of the change intervals (48, 72, and 108 seconds) to determine the number of times they change together in a minute.
In summary, word problems based on HCF and LCM require students to interpret the problem, identify the relevant information, and apply their knowledge of these concepts to find the answer. These problems can be found in various real-life scenarios and often involve both finding the HCF and LCM or using these concepts together to solve the problem.
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Description
Test your understanding of word problems involving Highest Common Factor (HCF) and Lowest Common Multiple (LCM). Practice interpreting the problem, identifying relevant information, and applying mathematical concepts to find the answer. Explore scenarios where HCF and LCM are crucial in real-life situations.
