Least Common Multiple (LCM) of 83 and 138
The least common multiple (LCM) of 83 and 138 is 11454.
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 138?
First, calculate the GCD of 83 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 138 = 0 remainder 83 |
| 2 | 138 ÷ 83 = 1 remainder 55 |
| 3 | 83 ÷ 55 = 1 remainder 28 |
| 4 | 55 ÷ 28 = 1 remainder 27 |
| 5 | 28 ÷ 27 = 1 remainder 1 |
| 6 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 138 | 11730 |
| 75 and 172 | 12900 |
| 186 and 27 | 1674 |
| 128 and 102 | 6528 |
| 105 and 20 | 420 |