Least Common Multiple (LCM) of 108 and 199
The least common multiple (LCM) of 108 and 199 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 108 and 199?
First, calculate the GCD of 108 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 199 = 0 remainder 108 |
| 2 | 199 ÷ 108 = 1 remainder 91 |
| 3 | 108 ÷ 91 = 1 remainder 17 |
| 4 | 91 ÷ 17 = 5 remainder 6 |
| 5 | 17 ÷ 6 = 2 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 105 | 17745 |
| 194 and 175 | 33950 |
| 32 and 36 | 288 |
| 25 and 120 | 600 |
| 49 and 18 | 882 |