Least Common Multiple (LCM) of 187 and 137
The least common multiple (LCM) of 187 and 137 is 25619.
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 137?
First, calculate the GCD of 187 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 137 = 1 remainder 50 |
| 2 | 137 ÷ 50 = 2 remainder 37 |
| 3 | 50 ÷ 37 = 1 remainder 13 |
| 4 | 37 ÷ 13 = 2 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 80 | 3120 |
| 50 and 60 | 300 |
| 173 and 39 | 6747 |
| 107 and 59 | 6313 |
| 55 and 108 | 5940 |