Least Common Multiple (LCM) of 137 and 80
The least common multiple (LCM) of 137 and 80 is 10960.
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 80?
First, calculate the GCD of 137 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 80 = 1 remainder 57 |
| 2 | 80 ÷ 57 = 1 remainder 23 |
| 3 | 57 ÷ 23 = 2 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 85 | 2550 |
| 103 and 32 | 3296 |
| 188 and 183 | 34404 |
| 87 and 32 | 2784 |
| 133 and 67 | 8911 |