Least Common Multiple (LCM) of 185 and 189
The least common multiple (LCM) of 185 and 189 is 34965.
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 185 and 189?
First, calculate the GCD of 185 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 189 = 0 remainder 185 |
| 2 | 189 ÷ 185 = 1 remainder 4 |
| 3 | 185 ÷ 4 = 46 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 34 | 714 |
| 180 and 37 | 6660 |
| 51 and 65 | 3315 |
| 119 and 126 | 2142 |
| 133 and 18 | 2394 |