Least Common Multiple (LCM) of 107 and 190
The least common multiple (LCM) of 107 and 190 is 20330.
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 107 and 190?
First, calculate the GCD of 107 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 190 = 0 remainder 107 |
| 2 | 190 ÷ 107 = 1 remainder 83 |
| 3 | 107 ÷ 83 = 1 remainder 24 |
| 4 | 83 ÷ 24 = 3 remainder 11 |
| 5 | 24 ÷ 11 = 2 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 23 | 2139 |
| 90 and 142 | 6390 |
| 189 and 141 | 8883 |
| 182 and 82 | 7462 |
| 38 and 200 | 3800 |