Least Common Multiple (LCM) of 109 and 185
The least common multiple (LCM) of 109 and 185 is 20165.
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 109 and 185?
First, calculate the GCD of 109 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 185 = 0 remainder 109 |
| 2 | 185 ÷ 109 = 1 remainder 76 |
| 3 | 109 ÷ 76 = 1 remainder 33 |
| 4 | 76 ÷ 33 = 2 remainder 10 |
| 5 | 33 ÷ 10 = 3 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 74 | 4958 |
| 96 and 81 | 2592 |
| 169 and 74 | 12506 |
| 27 and 55 | 1485 |
| 105 and 156 | 5460 |