Least Common Multiple (LCM) of 99 and 108
The least common multiple (LCM) of 99 and 108 is 1188.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 99 and 108?
First, calculate the GCD of 99 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 108 = 0 remainder 99 |
| 2 | 108 ÷ 99 = 1 remainder 9 |
| 3 | 99 ÷ 9 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 126 | 3906 |
| 96 and 139 | 13344 |
| 81 and 71 | 5751 |
| 27 and 69 | 621 |
| 180 and 168 | 2520 |