Least Common Multiple (LCM) of 138 and 86
The least common multiple (LCM) of 138 and 86 is 5934.
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 86?
First, calculate the GCD of 138 and 86 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 86 = 1 remainder 52 |
| 2 | 86 ÷ 52 = 1 remainder 34 |
| 3 | 52 ÷ 34 = 1 remainder 18 |
| 4 | 34 ÷ 18 = 1 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 156 | 6708 |
| 51 and 13 | 663 |
| 153 and 129 | 6579 |
| 107 and 41 | 4387 |
| 172 and 135 | 23220 |