Least Common Multiple (LCM) of 189 and 69
The least common multiple (LCM) of 189 and 69 is 4347.
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 69?
First, calculate the GCD of 189 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 69 = 2 remainder 51 |
| 2 | 69 ÷ 51 = 1 remainder 18 |
| 3 | 51 ÷ 18 = 2 remainder 15 |
| 4 | 18 ÷ 15 = 1 remainder 3 |
| 5 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 78 | 2106 |
| 150 and 70 | 1050 |
| 137 and 169 | 23153 |
| 21 and 49 | 147 |
| 15 and 141 | 705 |