Least Common Multiple (LCM) of 110 and 186
The least common multiple (LCM) of 110 and 186 is 10230.
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 110 and 186?
First, calculate the GCD of 110 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 186 = 0 remainder 110 |
| 2 | 186 ÷ 110 = 1 remainder 76 |
| 3 | 110 ÷ 76 = 1 remainder 34 |
| 4 | 76 ÷ 34 = 2 remainder 8 |
| 5 | 34 ÷ 8 = 4 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 72 | 3096 |
| 191 and 41 | 7831 |
| 13 and 29 | 377 |
| 59 and 180 | 10620 |
| 117 and 32 | 3744 |