Least Common Multiple (LCM) of 199 and 108
The least common multiple (LCM) of 199 and 108 is 21492.
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 199 and 108?
First, calculate the GCD of 199 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 108 = 1 remainder 91 |
| 2 | 108 ÷ 91 = 1 remainder 17 |
| 3 | 91 ÷ 17 = 5 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 120 | 960 |
| 19 and 140 | 2660 |
| 129 and 167 | 21543 |
| 113 and 89 | 10057 |
| 115 and 112 | 12880 |