Least Common Multiple (LCM) of 119 and 108
The least common multiple (LCM) of 119 and 108 is 12852.
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 119 and 108?
First, calculate the GCD of 119 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 108 = 1 remainder 11 |
| 2 | 108 ÷ 11 = 9 remainder 9 |
| 3 | 11 ÷ 9 = 1 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 184 | 22632 |
| 149 and 124 | 18476 |
| 115 and 139 | 15985 |
| 192 and 193 | 37056 |
| 49 and 104 | 5096 |