Least Common Multiple (LCM) of 114 and 139
The least common multiple (LCM) of 114 and 139 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 114 and 139?
First, calculate the GCD of 114 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 139 = 0 remainder 114 |
| 2 | 139 ÷ 114 = 1 remainder 25 |
| 3 | 114 ÷ 25 = 4 remainder 14 |
| 4 | 25 ÷ 14 = 1 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 54 | 1728 |
| 144 and 116 | 4176 |
| 199 and 153 | 30447 |
| 13 and 102 | 1326 |
| 12 and 112 | 336 |