Least Common Multiple (LCM) of 137 and 140
The least common multiple (LCM) of 137 and 140 is 19180.
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 140?
First, calculate the GCD of 137 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 140 = 0 remainder 137 |
| 2 | 140 ÷ 137 = 1 remainder 3 |
| 3 | 137 ÷ 3 = 45 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 82 | 4264 |
| 180 and 160 | 1440 |
| 176 and 44 | 176 |
| 105 and 179 | 18795 |
| 25 and 81 | 2025 |