Least Common Multiple (LCM) of 110 and 189
The least common multiple (LCM) of 110 and 189 is 20790.
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 189?
First, calculate the GCD of 110 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 189 = 0 remainder 110 |
| 2 | 189 ÷ 110 = 1 remainder 79 |
| 3 | 110 ÷ 79 = 1 remainder 31 |
| 4 | 79 ÷ 31 = 2 remainder 17 |
| 5 | 31 ÷ 17 = 1 remainder 14 |
| 6 | 17 ÷ 14 = 1 remainder 3 |
| 7 | 14 ÷ 3 = 4 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 196 | 10388 |
| 200 and 163 | 32600 |
| 120 and 100 | 600 |
| 173 and 189 | 32697 |
| 175 and 98 | 2450 |