Least Common Multiple (LCM) of 83 and 137
The least common multiple (LCM) of 83 and 137 is 11371.
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 83 and 137?
First, calculate the GCD of 83 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 137 = 0 remainder 83 |
| 2 | 137 ÷ 83 = 1 remainder 54 |
| 3 | 83 ÷ 54 = 1 remainder 29 |
| 4 | 54 ÷ 29 = 1 remainder 25 |
| 5 | 29 ÷ 25 = 1 remainder 4 |
| 6 | 25 ÷ 4 = 6 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 90 | 6390 |
| 43 and 90 | 3870 |
| 100 and 38 | 1900 |
| 161 and 51 | 8211 |
| 39 and 156 | 156 |