Least Common Multiple (LCM) of 122 and 189
The least common multiple (LCM) of 122 and 189 is 23058.
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 122 and 189?
First, calculate the GCD of 122 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 189 = 0 remainder 122 |
| 2 | 189 ÷ 122 = 1 remainder 67 |
| 3 | 122 ÷ 67 = 1 remainder 55 |
| 4 | 67 ÷ 55 = 1 remainder 12 |
| 5 | 55 ÷ 12 = 4 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 87 | 8700 |
| 28 and 97 | 2716 |
| 15 and 121 | 1815 |
| 66 and 61 | 4026 |
| 130 and 105 | 2730 |