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 |
|---|---|
| 189 and 30 | 1890 |
| 101 and 83 | 8383 |
| 151 and 49 | 7399 |
| 130 and 76 | 4940 |
| 151 and 190 | 28690 |