Least Common Multiple (LCM) of 138 and 187
The least common multiple (LCM) of 138 and 187 is 25806.
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 187?
First, calculate the GCD of 138 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 187 = 0 remainder 138 |
| 2 | 187 ÷ 138 = 1 remainder 49 |
| 3 | 138 ÷ 49 = 2 remainder 40 |
| 4 | 49 ÷ 40 = 1 remainder 9 |
| 5 | 40 ÷ 9 = 4 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 84 | 420 |
| 33 and 15 | 165 |
| 67 and 60 | 4020 |
| 135 and 81 | 405 |
| 87 and 156 | 4524 |