Least Common Multiple (LCM) of 199 and 138
The least common multiple (LCM) of 199 and 138 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 199 and 138?
First, calculate the GCD of 199 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 138 = 1 remainder 61 |
| 2 | 138 ÷ 61 = 2 remainder 16 |
| 3 | 61 ÷ 16 = 3 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 42 | 1260 |
| 174 and 156 | 4524 |
| 146 and 32 | 2336 |
| 173 and 94 | 16262 |
| 149 and 113 | 16837 |