Least Common Multiple (LCM) of 138 and 83
The least common multiple (LCM) of 138 and 83 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 138 and 83?
First, calculate the GCD of 138 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 83 = 1 remainder 55 |
| 2 | 83 ÷ 55 = 1 remainder 28 |
| 3 | 55 ÷ 28 = 1 remainder 27 |
| 4 | 28 ÷ 27 = 1 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 177 | 8142 |
| 180 and 137 | 24660 |
| 59 and 35 | 2065 |
| 150 and 94 | 7050 |
| 138 and 80 | 5520 |