Least Common Multiple (LCM) of 138 and 199
The least common multiple (LCM) of 138 and 199 is 27462.
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 199?
First, calculate the GCD of 138 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 199 = 0 remainder 138 |
| 2 | 199 ÷ 138 = 1 remainder 61 |
| 3 | 138 ÷ 61 = 2 remainder 16 |
| 4 | 61 ÷ 16 = 3 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 173 | 1730 |
| 111 and 91 | 10101 |
| 113 and 88 | 9944 |
| 90 and 200 | 1800 |
| 130 and 157 | 20410 |