Least Common Multiple (LCM) of 59 and 189
The least common multiple (LCM) of 59 and 189 is 11151.
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 59 and 189?
First, calculate the GCD of 59 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 189 = 0 remainder 59 |
| 2 | 189 ÷ 59 = 3 remainder 12 |
| 3 | 59 ÷ 12 = 4 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 162 | 19278 |
| 106 and 173 | 18338 |
| 124 and 103 | 12772 |
| 58 and 198 | 5742 |
| 169 and 123 | 20787 |