Least common multiple

Learning Objectives Define multiples, common multiples, and the Least Common Multiple (LCM). Find the LCM of two or more numbers by listing multiples. Find the LCM of two or more numbers using prime factorization. Explain the relationship between LCM and GCF. Apply the concept of LCM to solve real-world problems. Identify and correct common errors when calculating the LCM. Have you ever wondered when two buses on different schedules will arrive at the same stop at the exact same time again? 🚌 This lesson will help you solve puzzles like that! In this lesson, you'll discover what the Least Common Multiple (LCM) is and learn powerful methods to find it. Understanding LCM is crucial for solving problems involving cycles, scheduling, and combining quantities, making it a...

TermDefinitionExample MultipleA multiple of a number is the result of multiplying that number by an integer (like 1, 2, 3, etc.). It's like counting by that number.Multiples of 3 are: 3, 6, 9, 12, 15, 18, ... Common MultipleA common multiple of two or more numbers is a number that is a multiple of all of them.For 2 and 3, common multiples include 6, 12, 18, ... Least Common Multiple (LCM)The Least Common Multiple (LCM) of two or more non-zero integers is the smallest positive integer that is a multiple of all the numbers.The LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3. Prime NumberA prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and itself.2, 3, 5, 7, 11 are prime numbers. Prime FactorizationPrime f...

Finding LCM by Listing Multiples List the multiples of each number until you find the smallest multiple that appears in all lists. This method is effective for smaller numbers. Write out the multiples for each number, starting from the number itself, and identify the first common number you encounter. Finding LCM by Prime Factorization 1. Find the prime factorization of each number. 2. For each prime factor, take the highest power that appears in any of the factorizations. 3. Multiply these highest powers together. This method is generally more efficient for larger numbers. It ensures you include all necessary prime factors with their correct multiplicities to form the smallest common multiple. For example, if $A = p_1^{a_1} p_2^{a_2} \dots$ and $B = p_1^{b_1} p_2^{b_2} \dot...