Least Common Multiple (LCM) of 81 and 139
The least common multiple (LCM) of 81 and 139 is 11259.
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 81 and 139?
First, calculate the GCD of 81 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 139 = 0 remainder 81 |
| 2 | 139 ÷ 81 = 1 remainder 58 |
| 3 | 81 ÷ 58 = 1 remainder 23 |
| 4 | 58 ÷ 23 = 2 remainder 12 |
| 5 | 23 ÷ 12 = 1 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 40 | 1640 |
| 84 and 20 | 420 |
| 32 and 106 | 1696 |
| 38 and 100 | 1900 |
| 17 and 45 | 765 |