Least Common Multiple (LCM) of 69 and 185
The least common multiple (LCM) of 69 and 185 is 12765.
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 185?
First, calculate the GCD of 69 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 185 = 0 remainder 69 |
| 2 | 185 ÷ 69 = 2 remainder 47 |
| 3 | 69 ÷ 47 = 1 remainder 22 |
| 4 | 47 ÷ 22 = 2 remainder 3 |
| 5 | 22 ÷ 3 = 7 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 18 | 90 |
| 83 and 167 | 13861 |
| 104 and 78 | 312 |
| 16 and 14 | 112 |
| 195 and 189 | 12285 |