Least Common Multiple (LCM) of 139 and 199
The least common multiple (LCM) of 139 and 199 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 139 and 199?
First, calculate the GCD of 139 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 199 = 0 remainder 139 |
| 2 | 199 ÷ 139 = 1 remainder 60 |
| 3 | 139 ÷ 60 = 2 remainder 19 |
| 4 | 60 ÷ 19 = 3 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 96 | 864 |
| 140 and 93 | 13020 |
| 177 and 141 | 8319 |
| 167 and 120 | 20040 |
| 48 and 51 | 816 |