Least Common Multiple (LCM) of 189 and 119
The least common multiple (LCM) of 189 and 119 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 189 and 119?
First, calculate the GCD of 189 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 119 = 1 remainder 70 |
| 2 | 119 ÷ 70 = 1 remainder 49 |
| 3 | 70 ÷ 49 = 1 remainder 21 |
| 4 | 49 ÷ 21 = 2 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 139 | 25020 |
| 70 and 114 | 3990 |
| 180 and 161 | 28980 |
| 10 and 24 | 120 |
| 153 and 137 | 20961 |