Least Common Multiple (LCM) of 121 and 189
The least common multiple (LCM) of 121 and 189 is 22869.
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 121 and 189?
First, calculate the GCD of 121 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 189 = 0 remainder 121 |
| 2 | 189 ÷ 121 = 1 remainder 68 |
| 3 | 121 ÷ 68 = 1 remainder 53 |
| 4 | 68 ÷ 53 = 1 remainder 15 |
| 5 | 53 ÷ 15 = 3 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 60 | 8340 |
| 93 and 144 | 4464 |
| 23 and 71 | 1633 |
| 163 and 193 | 31459 |
| 158 and 181 | 28598 |