Least Common Multiple (LCM) of 185 and 118
The least common multiple (LCM) of 185 and 118 is 21830.
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 118?
First, calculate the GCD of 185 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 118 = 1 remainder 67 |
| 2 | 118 ÷ 67 = 1 remainder 51 |
| 3 | 67 ÷ 51 = 1 remainder 16 |
| 4 | 51 ÷ 16 = 3 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 72 | 1224 |
| 35 and 133 | 665 |
| 145 and 100 | 2900 |
| 101 and 48 | 4848 |
| 18 and 177 | 1062 |