Least Common Multiple (LCM) of 109 and 110
The least common multiple (LCM) of 109 and 110 is 11990.
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 109 and 110?
First, calculate the GCD of 109 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 110 = 0 remainder 109 |
| 2 | 110 ÷ 109 = 1 remainder 1 |
| 3 | 109 ÷ 1 = 109 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 172 | 33884 |
| 66 and 63 | 1386 |
| 74 and 32 | 1184 |
| 58 and 100 | 2900 |
| 162 and 200 | 16200 |