Least common multiple

Learning Objectives Define multiples, common multiples, and the Least Common Multiple (LCM). Identify multiples of given whole numbers. Calculate the LCM of two or more whole numbers by listing multiples. Calculate the LCM of two or more whole numbers using prime factorization. Apply the concept of LCM to solve real-world problems. Explain the difference between a common multiple and the least common multiple. Ever wondered when two different bus schedules will align, or when two friends will meet up again if they visit the library on different cycles? 🚌📚 In this lesson, you'll discover the Least Common Multiple (LCM), a powerful tool for finding the smallest 'meeting point' for numbers. Understanding LCM helps us solve problems where events repeat at diffe...

TermDefinitionExample MultipleA multiple of a number is the result of multiplying that number by any whole number (except zero). It's like counting by that number.Multiples of 3 are 3, 6, 9, 12, 15, ... 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 numbers is the smallest positive common multiple of those 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 only two positive factors: 1 and itself.2, 3, 5, 7, 11 are prime numbers. Prime FactorizationPrime factorization is the process of br...

Finding LCM by Listing Multiples 1. List the first few multiples of each number. 2. Identify the common multiples from the lists. 3. The smallest common multiple is the LCM. This method is good for smaller numbers or when you need to visualize the multiples. It directly applies the definition of LCM. Finding LCM by Prime Factorization 1. Find the prime factorization of each number. 2. For each unique prime factor, identify the highest power (exponent) that appears in any of the factorizations. 3. Multiply these highest powers together to get the LCM. This method is efficient for larger numbers and ensures you don't miss any factors. It uses the fundamental theorem of arithmetic.