Least Common Multiple (LCM) of 187 and 107
The least common multiple (LCM) of 187 and 107 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 187 and 107?
First, calculate the GCD of 187 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 107 = 1 remainder 80 |
| 2 | 107 ÷ 80 = 1 remainder 27 |
| 3 | 80 ÷ 27 = 2 remainder 26 |
| 4 | 27 ÷ 26 = 1 remainder 1 |
| 5 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 147 | 3528 |
| 110 and 85 | 1870 |
| 177 and 106 | 18762 |
| 166 and 133 | 22078 |
| 15 and 63 | 315 |