Finding the Least Common Multiple (LCM)
The Least Common Multiple (LCM) is the smallest positive integer that is perfectly divisible by two or more numbers. It is a foundational concept in algebra, particularly when adding or subtracting fractions with different denominators.
The Prime Factorization Method
To find the LCM manually, find the prime factors of each number. Then, multiply each prime factor the greatest number of times it occurs in either number. For example, LCM of 12 (2² × 3) and 15 (3 × 5) is 2² × 3 × 5 = 60.
Real World Uses
LCM is used in planetary alignments, scheduling overlapping events, and digital cryptography algorithms. If Bus A arrives every 15 minutes and Bus B every 20 minutes, the LCM (60 minutes) tells you they will arrive simultaneously every hour.