Definition: The least common multiple of two or more whole numbers is the smallest positive number that is a multiple of every one of them.
What is the LCM?
A multiple of a number is what you get by multiplying it by 1, 2, 3, and so on. The LCM is the first multiple that two numbers share.
How do you find it?
List multiples. For 9 and 12:
- Multiples of 9: 9, 18, 27, 36, 45
- Multiples of 12: 12, 24, 36, 48
The smallest shared multiple is 36.
With prime factorization, 9 = 32 and 12 = 22 x 3. Take the highest power of each prime: 22 x 32 = 36.
When does it help?
Two lights flash at different intervals. One blinks every 9 seconds and the other every 12 seconds. They blink together every 36 seconds. The LCM is also the best common denominator when you add fractions like 5/9 + 7/12.
What is the common error?
Multiplying the numbers and stopping. 9 x 12 = 108 is a common multiple, but not the least one.