Least Common Multiple
The Least Common Multiple (LCM) is the smallest positive number that is a multiple of two or more given numbers. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students find the LCM using two methods: listing multiples (write out the first several multiples of each number and identify the smallest one that appears in all lists), or prime factorization (find the prime factors of each number and take the highest power of each prime). The LCM of 8 and 12 is 24. The LCM is also used to find the Least Common Denominator when adding fractions.
Key Concepts
Property The smallest positive number that is a multiple of two or more numbers is the least common multiple (LCM).
Examples The LCM of 3 and 4 is 12, since their multiples are (3, 6, 9, 12 ) and (4, 8, 12 ). The LCM of 2 and 4 is 4, since their multiples are (2, 4 , 6) and ( 4 , 8, 12). The LCM of 4 and 6 is 12, since their multiples are (4, 8, 12 ) and (6, 12 , 18).
Explanation Imagine two friends racing on a track, but running at different speeds. The LCM is like the first spot on the track where they meet up again after starting! It's the smallest number that both of their numbers can 'land' on perfectly when you count up.
Common Questions
What is the Least Common Multiple (LCM)?
The LCM is the smallest positive integer that is divisible by each of the given numbers. For example, the LCM of 4 and 6 is 12.
How do you find the LCM by listing multiples?
List the first several multiples of each number. The LCM is the smallest number that appears in all the lists. For 4 and 6: multiples of 4 are 4, 8, 12, 16; multiples of 6 are 6, 12, 18. LCM = 12.
How do you find the LCM using prime factorization?
Find the prime factors of each number. Take the highest power of each prime that appears. Multiply these together. For 8=2³ and 12=2²×3: LCM = 2³ × 3 = 24.
What is the LCM of 5 and 7?
Since 5 and 7 are both prime, their LCM is simply 5 × 7 = 35.
How is the LCM used with fractions?
The LCM of the denominators is the Least Common Denominator (LCD) needed to add or subtract fractions with unlike denominators.