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In the field of mathematics, many concepts and tools help us solve real-life mathematical problems. One of these concepts is the Least Common Multiple, also known as LCM. As its name suggests, it is related to multiples. In this blog, we'll discuss all about LCM and delve into its utility in real-life problems.
What is LCM?
LCM is the least common multiple. It is an important concept that leads us to the smallest number that can be divided by two or more numbers perfectly. Calculating the Least Common multiple is quite easy. You need to find the multiples then look for the smallest common multiple. For example, the LCM of 4 and 6 is 12 which means 12 is the smallest number that can be divided by both 4 and 6.
Use of LCM
1. Finding Common Denominators
Comparing fractions and operations with fractions needs to make the denominator the same. LCM is the tool that helps us to find that one out. It is used to simplify the calculations involving fractions.
2. Solving Fractional Equations
When solving equations involving fractions, finding the LCM of the denominators helps in simplifying the equations and finding the correct solution.
3. Time and Motion Problems
Important concepts like time, distance, and speed always require LCM to be used to find the common intervals of two or more events.
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How is it Different from GCF?
GCF is the greatest common factor. LCM and GCF are entirely different from each other. GCF is used to find out the greatest number that can divide two or more given numbers. LCM and GCF are inverse to each other as one helps to find the multiple and the second helps to find the factor.
Real-Life Word Problems with Solutions Regarding LCM
Problem 1: Alice and Bob are planning a meeting. Alice is available every 4 days, and Bob is available every 6 days. When is the next day they can both meet?
Solution: Find the LCM of 4 and 6, which is 12. Therefore, they can meet every 12 days (about 1 week 5 days).
Problem 2: A painter paints every 8 days, while another painter paints every 12 days (about 1 week 5 days). How often do they meet if they start painting on the same day?
Solution: The LCM of 8 and 12 is 24. They will meet every 24 days (about 3 and a half weeks).
FAQs on LCM
Q1: Why do we use the least common multiple?
Ans: Least Common Multiple (LCM) is used to find common denominators, solve fractional equations, and manage time-related problems efficiently.
Q2: Where is the least common multiple used?
Ans: The LCM finds applications in mathematics, scheduling, engineering, and finance for tasks such as simplifying calculations, scheduling events, designing patterns, and financial calculations.
Q3: Is the lowest common multiple always 1?
Ans: No, the Lowest Common Multiple (LCM) is never 1 for positive integers; it is always greater than or equal to the largest of those integers.
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In conclusion, the Least Common Multiple (LCM) is a fundamental concept in mathematics with practical applications in various fields. It aids in finding common denominators, solving fractional equations, and tackling real-world problems involving time, scheduling, and resource management. Understanding LCM and its role in problem-solving equips us with valuable tools for efficient mathematical analysis and decision-making.
