Least Common Multiple (LCM) of 185 and 109
The least common multiple (LCM) of 185 and 109 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 185 and 109?
First, calculate the GCD of 185 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 109 = 1 remainder 76 |
| 2 | 109 ÷ 76 = 1 remainder 33 |
| 3 | 76 ÷ 33 = 2 remainder 10 |
| 4 | 33 ÷ 10 = 3 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 102 | 6834 |
| 122 and 117 | 14274 |
| 23 and 67 | 1541 |
| 78 and 23 | 1794 |
| 43 and 17 | 731 |