Least Common Multiple (LCM) of 108 and 139
The least common multiple (LCM) of 108 and 139 is 15012.
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 108 and 139?
First, calculate the GCD of 108 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 139 = 0 remainder 108 |
| 2 | 139 ÷ 108 = 1 remainder 31 |
| 3 | 108 ÷ 31 = 3 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 135 | 540 |
| 105 and 188 | 19740 |
| 13 and 107 | 1391 |
| 102 and 177 | 6018 |
| 12 and 156 | 156 |