Least Common Multiple (LCM) of 83 and 139
The least common multiple (LCM) of 83 and 139 is 11537.
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 83 and 139?
First, calculate the GCD of 83 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 139 = 0 remainder 83 |
| 2 | 139 ÷ 83 = 1 remainder 56 |
| 3 | 83 ÷ 56 = 1 remainder 27 |
| 4 | 56 ÷ 27 = 2 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 75 | 300 |
| 15 and 165 | 165 |
| 53 and 103 | 5459 |
| 22 and 188 | 2068 |
| 90 and 43 | 3870 |