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 |
|---|---|
| 168 and 117 | 6552 |
| 23 and 139 | 3197 |
| 56 and 111 | 6216 |
| 71 and 25 | 1775 |
| 105 and 53 | 5565 |