Least Common Multiple (LCM) of 123 and 181
The least common multiple (LCM) of 123 and 181 is 22263.
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 123 and 181?
First, calculate the GCD of 123 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 181 = 0 remainder 123 |
| 2 | 181 ÷ 123 = 1 remainder 58 |
| 3 | 123 ÷ 58 = 2 remainder 7 |
| 4 | 58 ÷ 7 = 8 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 133 | 1596 |
| 17 and 29 | 493 |
| 170 and 72 | 6120 |
| 180 and 134 | 12060 |
| 131 and 73 | 9563 |