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. Solve real-world problems that require finding the LCM. Explain the significance of the LCM in practical situations. Distinguish between finding the LCM and other number theory concepts like factors. Have you ever wondered when two events will happen at the same time again? ⏰ Like two buses arriving together or two friends meeting up at the same spot? In this lesson, you'll learn about the Least Common Multiple (LCM), a powerful tool to find the smallest number that is a multiple of two or more given numbers. This skill helps us solve problems where things r...

TermDefinitionExample MultipleA multiple of a number is the result of multiplying that number by any whole number (except zero).Multiples of 5 are 5, 10, 15, 20, 25, ... Common MultipleA common multiple of two or more numbers is a number that is a multiple of all of them.12 is a common multiple of 3 and 4, because 12 = 3 x 4 and 12 = 4 x 3. Least Common Multiple (LCM)The Least Common Multiple (LCM) is the smallest positive common multiple of two or more numbers.The LCM of 3 and 4 is 12, because it's the smallest number that appears in both lists of multiples (Multiples of 3: 3, 6, 9, 12, ...; Multiples of 4: 4, 8, 12, ...). FactorA factor of a number is a whole number that divides into it exactly, without leaving a remainder.The factors of 12 are 1, 2, 3, 4, 6, and 12. Prime NumberA...

Method 1: Listing Multiples To find the LCM of two or more numbers, list out the multiples of each number until you find the smallest number that appears in all lists. This method is effective for finding the LCM of smaller numbers. You write down the multiples of each number in increasing order and identify the first number that is common to all lists. Method 2: Prime Factorization 1. Find the prime factorization of each number. 2. For each unique prime factor, identify the highest power (exponent) it has in any of the factorizations. 3. Multiply these highest powers together to get the LCM. This method is efficient for finding the LCM of larger numbers. It breaks down each number into its prime building blocks, then combines them to form the smallest number divisible by al...