Least Common Multiple (LCM) of 155 and 189
The least common multiple (LCM) of 155 and 189 is 29295.
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 155 and 189?
First, calculate the GCD of 155 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 189 = 0 remainder 155 |
| 2 | 189 ÷ 155 = 1 remainder 34 |
| 3 | 155 ÷ 34 = 4 remainder 19 |
| 4 | 34 ÷ 19 = 1 remainder 15 |
| 5 | 19 ÷ 15 = 1 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 146 | 17958 |
| 113 and 197 | 22261 |
| 198 and 44 | 396 |
| 104 and 113 | 11752 |
| 145 and 135 | 3915 |