Least Common Multiple (LCM) of 110 and 119
The least common multiple (LCM) of 110 and 119 is 13090.
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 119?
First, calculate the GCD of 110 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 119 = 0 remainder 110 |
| 2 | 119 ÷ 110 = 1 remainder 9 |
| 3 | 110 ÷ 9 = 12 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 54 | 270 |
| 39 and 191 | 7449 |
| 14 and 74 | 518 |
| 10 and 20 | 20 |
| 51 and 23 | 1173 |