Least Common Multiple (LCM) of 110 and 89
The least common multiple (LCM) of 110 and 89 is 9790.
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 89?
First, calculate the GCD of 110 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 89 = 1 remainder 21 |
| 2 | 89 ÷ 21 = 4 remainder 5 |
| 3 | 21 ÷ 5 = 4 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 39 | 1989 |
| 21 and 75 | 525 |
| 154 and 105 | 2310 |
| 132 and 158 | 10428 |
| 100 and 54 | 2700 |