Least Common Multiple (LCM) of 137 and 187
The least common multiple (LCM) of 137 and 187 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 137 and 187?
First, calculate the GCD of 137 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 187 = 0 remainder 137 |
| 2 | 187 ÷ 137 = 1 remainder 50 |
| 3 | 137 ÷ 50 = 2 remainder 37 |
| 4 | 50 ÷ 37 = 1 remainder 13 |
| 5 | 37 ÷ 13 = 2 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 117 | 2340 |
| 177 and 189 | 11151 |
| 64 and 64 | 64 |
| 55 and 75 | 825 |
| 153 and 70 | 10710 |