Least Common Multiple (LCM) of 189 and 114
The least common multiple (LCM) of 189 and 114 is 7182.
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 114?
First, calculate the GCD of 189 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 114 = 1 remainder 75 |
| 2 | 114 ÷ 75 = 1 remainder 39 |
| 3 | 75 ÷ 39 = 1 remainder 36 |
| 4 | 39 ÷ 36 = 1 remainder 3 |
| 5 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 84 | 3948 |
| 45 and 83 | 3735 |
| 163 and 14 | 2282 |
| 30 and 136 | 2040 |
| 12 and 163 | 1956 |