Least Common Multiple (LCM) of 125 and 137
The least common multiple (LCM) of 125 and 137 is 17125.
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 125 and 137?
First, calculate the GCD of 125 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 137 = 0 remainder 125 |
| 2 | 137 ÷ 125 = 1 remainder 12 |
| 3 | 125 ÷ 12 = 10 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 59 | 10207 |
| 171 and 45 | 855 |
| 77 and 66 | 462 |
| 183 and 183 | 183 |
| 194 and 57 | 11058 |