Least Common Multiple (LCM) of 137 and 125
The least common multiple (LCM) of 137 and 125 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 137 and 125?
First, calculate the GCD of 137 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 125 = 1 remainder 12 |
| 2 | 125 ÷ 12 = 10 remainder 5 |
| 3 | 12 ÷ 5 = 2 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 107 | 2033 |
| 39 and 168 | 2184 |
| 112 and 116 | 3248 |
| 173 and 189 | 32697 |
| 134 and 64 | 4288 |