Least Common Multiple (LCM) of 139 and 85
The least common multiple (LCM) of 139 and 85 is 11815.
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 85?
First, calculate the GCD of 139 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 85 = 1 remainder 54 |
| 2 | 85 ÷ 54 = 1 remainder 31 |
| 3 | 54 ÷ 31 = 1 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 139 | 15846 |
| 189 and 55 | 10395 |
| 110 and 14 | 770 |
| 99 and 60 | 1980 |
| 52 and 77 | 4004 |