Least Common Multiple (LCM) of 137 and 185
The least common multiple (LCM) of 137 and 185 is 25345.
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 185?
First, calculate the GCD of 137 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 185 = 0 remainder 137 |
| 2 | 185 ÷ 137 = 1 remainder 48 |
| 3 | 137 ÷ 48 = 2 remainder 41 |
| 4 | 48 ÷ 41 = 1 remainder 7 |
| 5 | 41 ÷ 7 = 5 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 14 | 378 |
| 41 and 51 | 2091 |
| 120 and 114 | 2280 |
| 158 and 53 | 8374 |
| 175 and 104 | 18200 |