Least Common Multiple (LCM) of 68 and 189
The least common multiple (LCM) of 68 and 189 is 12852.
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 68 and 189?
First, calculate the GCD of 68 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 189 = 0 remainder 68 |
| 2 | 189 ÷ 68 = 2 remainder 53 |
| 3 | 68 ÷ 53 = 1 remainder 15 |
| 4 | 53 ÷ 15 = 3 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 12 | 204 |
| 59 and 199 | 11741 |
| 103 and 130 | 13390 |
| 127 and 182 | 23114 |
| 142 and 188 | 13348 |