Least Common Multiple (LCM) of 137 and 81
The least common multiple (LCM) of 137 and 81 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 137 and 81?
First, calculate the GCD of 137 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 81 = 1 remainder 56 |
| 2 | 81 ÷ 56 = 1 remainder 25 |
| 3 | 56 ÷ 25 = 2 remainder 6 |
| 4 | 25 ÷ 6 = 4 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 143 | 16445 |
| 31 and 83 | 2573 |
| 25 and 159 | 3975 |
| 188 and 200 | 9400 |
| 145 and 89 | 12905 |