Least Common Multiple (LCM) of 80 and 137
The least common multiple (LCM) of 80 and 137 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 80 and 137?
First, calculate the GCD of 80 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 137 = 0 remainder 80 |
| 2 | 137 ÷ 80 = 1 remainder 57 |
| 3 | 80 ÷ 57 = 1 remainder 23 |
| 4 | 57 ÷ 23 = 2 remainder 11 |
| 5 | 23 ÷ 11 = 2 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 13 | 351 |
| 182 and 142 | 12922 |
| 42 and 91 | 546 |
| 177 and 26 | 4602 |
| 129 and 16 | 2064 |