LCM: Lowest Common Multiple

Learning Objectives Define what a multiple and a common multiple are. Explain the concept of the Lowest Common Multiple (LCM). Calculate the LCM of two or more numbers by listing multiples. Calculate the LCM of two or more numbers using prime factorization. Apply the LCM to solve real-world problems. Distinguish between LCM and GCF (Greatest Common Factor). Have you ever wondered when two events will happen at the exact same time again, like two buses arriving at a station? 🚌🚌 The Lowest Common Multiple (LCM) helps us figure out exactly that! In this lesson, you'll learn what the Lowest Common Multiple (LCM) is and discover powerful methods to find it for any set of numbers. Understanding LCM is crucial for solving problems involving cycles, timing, and fractions, bu...

TermDefinitionExample MultipleThe result of multiplying a number by any non-zero whole number. It's like counting by that number.Multiples of 4 are 4, 8, 12, 16, 20, ... Common MultipleA number that is a multiple of two or more different numbers.12 is a common multiple of 3 and 4 because 12 is a multiple of 3 (3x4) and a multiple of 4 (4x3). Lowest Common Multiple (LCM)The smallest positive common multiple of two or more numbers. It's the smallest number that all the given numbers can divide into evenly.The LCM of 3 and 4 is 12, as it's the smallest number that is a multiple of both 3 and 4. Prime NumberA whole number greater than 1 that has exactly two positive divisors: 1 and itself.2, 3, 5, 7, 11, 13 are prime numbers. Composite NumberA whole number greater than 1 that h...

Listing Multiples Method for LCM To find the LCM of two or more numbers, list out the multiples of each number in ascending order until you find the smallest multiple that appears in all lists. This method is straightforward and effective for finding the LCM of smaller numbers. You simply write down the multiples for each number and identify the first number that is common to all lists. Prime Factorization Method for LCM To find the LCM of two or more numbers using prime factorization, first find the prime factorization of each number. Then, for each unique prime factor, take the highest power (the one with the largest exponent) that appears in any of the factorizations and multiply these highest powers together. This method is generally more efficient and reliable for large...