How to find a COMMON MULTIPLE of two numbers.
The product of two numbers is the easiest common multiple to find, but it is not always the least common multiple.
Ex: What is the least common multile of 28 and 42?
- 28 = 2 x 2 x 7
- 42 = 2 x 3 x 7
The LCM can be found by finding the prime factorization of each number, then seeing the greatest number of times each factor is used. Multiply each prime fctor the greatest number of times it appears.
In 28, 2 is used twice. In 42, 2 is used once. In 28, 7 is used once. In 42, seven is used once, and 3 is used once.
Thus, multiply each factor the greatest number of times it appears in a prime factorization:
LCM = 2 x 2 x 3 x 7 = 84