Least Common Multiple (LCM) of 149 and 189
The least common multiple (LCM) of 149 and 189 is 28161.
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 149 and 189?
First, calculate the GCD of 149 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 189 = 0 remainder 149 |
| 2 | 189 ÷ 149 = 1 remainder 40 |
| 3 | 149 ÷ 40 = 3 remainder 29 |
| 4 | 40 ÷ 29 = 1 remainder 11 |
| 5 | 29 ÷ 11 = 2 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 44 | 2156 |
| 66 and 186 | 2046 |
| 89 and 190 | 16910 |
| 75 and 140 | 2100 |
| 130 and 142 | 9230 |