Least Common Multiple (LCM) of 185 and 169
The least common multiple (LCM) of 185 and 169 is 31265.
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 169?
First, calculate the GCD of 185 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 169 = 1 remainder 16 |
| 2 | 169 ÷ 16 = 10 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 172 | 3612 |
| 186 and 25 | 4650 |
| 129 and 199 | 25671 |
| 115 and 34 | 3910 |
| 193 and 31 | 5983 |