Least Common Multiple (LCM) of 34 and 189
The least common multiple (LCM) of 34 and 189 is 6426.
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 34 and 189?
First, calculate the GCD of 34 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 189 = 0 remainder 34 |
| 2 | 189 ÷ 34 = 5 remainder 19 |
| 3 | 34 ÷ 19 = 1 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 119 | 13090 |
| 187 and 134 | 25058 |
| 63 and 161 | 1449 |
| 197 and 133 | 26201 |
| 165 and 120 | 1320 |