Least Common Multiple (LCM) of 190 and 107
The least common multiple (LCM) of 190 and 107 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 190 and 107?
First, calculate the GCD of 190 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 107 = 1 remainder 83 |
| 2 | 107 ÷ 83 = 1 remainder 24 |
| 3 | 83 ÷ 24 = 3 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 42 | 714 |
| 123 and 62 | 7626 |
| 104 and 101 | 10504 |
| 111 and 114 | 4218 |
| 31 and 148 | 4588 |