Least Common Multiple (LCM) of 189 and 121
The least common multiple (LCM) of 189 and 121 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 189 and 121?
First, calculate the GCD of 189 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 121 = 1 remainder 68 |
| 2 | 121 ÷ 68 = 1 remainder 53 |
| 3 | 68 ÷ 53 = 1 remainder 15 |
| 4 | 53 ÷ 15 = 3 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 75 | 525 |
| 153 and 113 | 17289 |
| 196 and 152 | 7448 |
| 19 and 129 | 2451 |
| 49 and 186 | 9114 |