Least Common Multiple (LCM) of 69 and 189
The least common multiple (LCM) of 69 and 189 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 69 and 189?
First, calculate the GCD of 69 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 189 = 0 remainder 69 |
| 2 | 189 ÷ 69 = 2 remainder 51 |
| 3 | 69 ÷ 51 = 1 remainder 18 |
| 4 | 51 ÷ 18 = 2 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 117 | 11700 |
| 96 and 175 | 16800 |
| 140 and 194 | 13580 |
| 78 and 44 | 1716 |
| 57 and 109 | 6213 |