Least Common Multiple (LCM) of 139 and 114
The least common multiple (LCM) of 139 and 114 is 15846.
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 114?
First, calculate the GCD of 139 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 114 = 1 remainder 25 |
| 2 | 114 ÷ 25 = 4 remainder 14 |
| 3 | 25 ÷ 14 = 1 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 192 | 1344 |
| 106 and 164 | 8692 |
| 86 and 71 | 6106 |
| 101 and 199 | 20099 |
| 37 and 78 | 2886 |