Least Common Multiple (LCM) of 115 and 139
The least common multiple (LCM) of 115 and 139 is 15985.
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 115 and 139?
First, calculate the GCD of 115 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 139 = 0 remainder 115 |
| 2 | 139 ÷ 115 = 1 remainder 24 |
| 3 | 115 ÷ 24 = 4 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 189 | 18333 |
| 97 and 11 | 1067 |
| 102 and 55 | 5610 |
| 126 and 128 | 8064 |
| 51 and 157 | 8007 |