Least Common Multiple (LCM) of 145 and 185
The least common multiple (LCM) of 145 and 185 is 5365.
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 145 and 185?
First, calculate the GCD of 145 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 185 = 0 remainder 145 |
| 2 | 185 ÷ 145 = 1 remainder 40 |
| 3 | 145 ÷ 40 = 3 remainder 25 |
| 4 | 40 ÷ 25 = 1 remainder 15 |
| 5 | 25 ÷ 15 = 1 remainder 10 |
| 6 | 15 ÷ 10 = 1 remainder 5 |
| 7 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 48 | 336 |
| 116 and 196 | 5684 |
| 84 and 200 | 4200 |
| 60 and 117 | 2340 |
| 133 and 132 | 17556 |