Lowest Common Multiple: LCM (In Steps)

Learning Objectives Identify and list multiples of a given whole number. Define and identify common multiples of two or more whole numbers. Determine the Lowest Common Multiple (LCM) of two or three whole numbers using the listing multiples method. Determine the Lowest Common Multiple (LCM) of two or three whole numbers using the prime factorization method. Apply the concept of LCM to solve real-world problems. Explain the significance of LCM in everyday situations. Ever wondered when two buses will arrive at the same stop at the same time again, or when two events will next happen together? 🚌⏰ That's where the Lowest Common Multiple helps us! In this lesson, you'll learn what the Lowest Common Multiple (LCM) is and discover step-by-step methods to find it for d...

TermDefinitionExample NumberA count or measurement that can be represented by a numeral. In this lesson, we focus on whole numbers (0, 1, 2, 3...).5, 12, 100 are all numbers. MultipleThe result of multiplying a number by an integer. It's like counting by that number.Multiples of 3 are 3, 6, 9, 12, 15, ... (3x1, 3x2, 3x3, ...) Common MultipleA number that is a multiple of two or more different numbers.For 2 and 3, common multiples include 6, 12, 18, ... (6 is a multiple of 2 and 3). 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.For 2 and 3, the multiples of 2 are {2, 4, **6**, 8, 10, **12**, ...} and multiples of 3 are {3, **6**, 9, **12**, 15, ...}. The common m...

Finding LCM by Listing Multiples To find the LCM of two or more numbers, list the multiples of each number until you find the smallest multiple that appears in all lists. This method is good for smaller numbers. Step 1: List the first few multiples of each number. Step 2: Identify the common multiples from the lists. Step 3: The smallest common multiple is the LCM. Example: $LCM(4, 6)$ Multiples of 4: $4, 8, \textbf{12}, 16, 20, \textbf{24}, \dots$ Multiples of 6: $6, \textbf{12}, 18, \textbf{24}, 30, \dots$ Common multiples: $12, 24, \dots$ Lowest Common Multiple: $12$ Finding LCM by Prime Factorization To find the LCM of two or more numbers: 1. Find the prime factorization of each number. 2. For each distinct prime factor, take the highest power (exponent) that appears in an...