Least Common Multiple (LCM) of 146 and 189
The least common multiple (LCM) of 146 and 189 is 27594.
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 146 and 189?
First, calculate the GCD of 146 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 189 = 0 remainder 146 |
| 2 | 189 ÷ 146 = 1 remainder 43 |
| 3 | 146 ÷ 43 = 3 remainder 17 |
| 4 | 43 ÷ 17 = 2 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 196 | 3724 |
| 172 and 64 | 2752 |
| 91 and 144 | 13104 |
| 101 and 163 | 16463 |
| 190 and 150 | 2850 |