Least Common Multiple (LCM) of 107 and 188
The least common multiple (LCM) of 107 and 188 is 20116.
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 188?
First, calculate the GCD of 107 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 188 = 0 remainder 107 |
| 2 | 188 ÷ 107 = 1 remainder 81 |
| 3 | 107 ÷ 81 = 1 remainder 26 |
| 4 | 81 ÷ 26 = 3 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 78 | 1326 |
| 15 and 37 | 555 |
| 196 and 70 | 980 |
| 101 and 127 | 12827 |
| 10 and 94 | 470 |