Least Common Multiple (LCM) of 139 and 189
The least common multiple (LCM) of 139 and 189 is 26271.
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 189?
First, calculate the GCD of 139 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 189 = 0 remainder 139 |
| 2 | 189 ÷ 139 = 1 remainder 50 |
| 3 | 139 ÷ 50 = 2 remainder 39 |
| 4 | 50 ÷ 39 = 1 remainder 11 |
| 5 | 39 ÷ 11 = 3 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 34 | 1394 |
| 33 and 42 | 462 |
| 13 and 158 | 2054 |
| 193 and 128 | 24704 |
| 21 and 135 | 945 |