Least Common Multiple (LCM) of 81 and 137
The least common multiple (LCM) of 81 and 137 is 11097.
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 81 and 137?
First, calculate the GCD of 81 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 137 = 0 remainder 81 |
| 2 | 137 ÷ 81 = 1 remainder 56 |
| 3 | 81 ÷ 56 = 1 remainder 25 |
| 4 | 56 ÷ 25 = 2 remainder 6 |
| 5 | 25 ÷ 6 = 4 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 67 | 5025 |
| 102 and 49 | 4998 |
| 26 and 136 | 1768 |
| 186 and 194 | 18042 |
| 178 and 38 | 3382 |