Least Common Multiple (LCM) of 110 and 188
The least common multiple (LCM) of 110 and 188 is 10340.
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 188?
First, calculate the GCD of 110 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 188 = 0 remainder 110 |
| 2 | 188 ÷ 110 = 1 remainder 78 |
| 3 | 110 ÷ 78 = 1 remainder 32 |
| 4 | 78 ÷ 32 = 2 remainder 14 |
| 5 | 32 ÷ 14 = 2 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 45 | 315 |
| 82 and 92 | 3772 |
| 15 and 117 | 585 |
| 113 and 182 | 20566 |
| 54 and 37 | 1998 |