Least Common Multiple (LCM) of 107 and 81
The least common multiple (LCM) of 107 and 81 is 8667.
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 81?
First, calculate the GCD of 107 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 81 = 1 remainder 26 |
| 2 | 81 ÷ 26 = 3 remainder 3 |
| 3 | 26 ÷ 3 = 8 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 52 | 1820 |
| 150 and 89 | 13350 |
| 149 and 180 | 26820 |
| 96 and 81 | 2592 |
| 156 and 74 | 5772 |