Least Common Multiple (LCM) of 107 and 187
The least common multiple (LCM) of 107 and 187 is 20009.
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 187?
First, calculate the GCD of 107 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 187 = 0 remainder 107 |
| 2 | 187 ÷ 107 = 1 remainder 80 |
| 3 | 107 ÷ 80 = 1 remainder 27 |
| 4 | 80 ÷ 27 = 2 remainder 26 |
| 5 | 27 ÷ 26 = 1 remainder 1 |
| 6 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 69 | 414 |
| 196 and 176 | 8624 |
| 39 and 18 | 234 |
| 60 and 185 | 2220 |
| 137 and 33 | 4521 |