Least Common Multiple (LCM) of 199 and 139
The least common multiple (LCM) of 199 and 139 is 27661.
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 139?
First, calculate the GCD of 199 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 139 = 1 remainder 60 |
| 2 | 139 ÷ 60 = 2 remainder 19 |
| 3 | 60 ÷ 19 = 3 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 199 | 23283 |
| 65 and 192 | 12480 |
| 143 and 158 | 22594 |
| 127 and 187 | 23749 |
| 75 and 140 | 2100 |