Least Common Multiple (LCM) of 189 and 68
The least common multiple (LCM) of 189 and 68 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 189 and 68?
First, calculate the GCD of 189 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 68 = 2 remainder 53 |
| 2 | 68 ÷ 53 = 1 remainder 15 |
| 3 | 53 ÷ 15 = 3 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 54 | 1998 |
| 25 and 43 | 1075 |
| 95 and 139 | 13205 |
| 136 and 19 | 2584 |
| 126 and 177 | 7434 |