Finding the Least Common Multiple
Find the Least Common Multiple (LCM) of numbers and polynomials in Grade 9 algebra using prime factorization or listing multiples, essential for adding and subtracting fractions with different denominators.
Key Concepts
New Concept The least number that is evenly divisible by each of the numbers in a set of numbers is called the least common multiple or LCM . What’s next Next, you'll use prime factorization to find the LCM for sets of numbers and then for algebraic expressions.
Common Questions
What is the LCM and how do you find it?
The LCM is the smallest number evenly divisible by each number in a set. Method 1: List multiples of each number until a common one appears. Method 2: Prime factorize all numbers, then take the highest power of each prime factor.
How do you find the LCM of 12 and 18 using prime factorization?
12 = 2² × 3 and 18 = 2 × 3². Take the highest power of each prime: 2² and 3². LCM = 2² × 3² = 4 × 9 = 36. Check: 36 ÷ 12 = 3 ✓ and 36 ÷ 18 = 2 ✓.
How is the LCM used when adding fractions with different denominators?
The LCM of the denominators is the Least Common Denominator (LCD). Convert each fraction to an equivalent fraction with the LCD, then add the numerators. For 1/4 + 1/6: LCM(4,6) = 12, so 3/12 + 2/12 = 5/12.