Least Common Multiple (LCM) of 119 and 189
The least common multiple (LCM) of 119 and 189 is 3213.
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 119 and 189?
First, calculate the GCD of 119 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 189 = 0 remainder 119 |
| 2 | 189 ÷ 119 = 1 remainder 70 |
| 3 | 119 ÷ 70 = 1 remainder 49 |
| 4 | 70 ÷ 49 = 1 remainder 21 |
| 5 | 49 ÷ 21 = 2 remainder 7 |
| 6 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 105 | 840 |
| 97 and 129 | 12513 |
| 51 and 31 | 1581 |
| 166 and 182 | 15106 |
| 165 and 57 | 3135 |