Least Common Multiple (LCM) of 137 and 83
The least common multiple (LCM) of 137 and 83 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 137 and 83?
First, calculate the GCD of 137 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 83 = 1 remainder 54 |
| 2 | 83 ÷ 54 = 1 remainder 29 |
| 3 | 54 ÷ 29 = 1 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 106 | 1060 |
| 127 and 197 | 25019 |
| 68 and 146 | 4964 |
| 157 and 71 | 11147 |
| 99 and 153 | 1683 |