Least Common Multiple (LCM) of 107 and 139
The least common multiple (LCM) of 107 and 139 is 14873.
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 107 and 139?
First, calculate the GCD of 107 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 139 = 0 remainder 107 |
| 2 | 139 ÷ 107 = 1 remainder 32 |
| 3 | 107 ÷ 32 = 3 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 71 | 14129 |
| 83 and 15 | 1245 |
| 87 and 131 | 11397 |
| 75 and 67 | 5025 |
| 163 and 96 | 15648 |