Least Common Multiple (LCM) of 110 and 23
The least common multiple (LCM) of 110 and 23 is 2530.
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 23?
First, calculate the GCD of 110 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 23 = 4 remainder 18 |
| 2 | 23 ÷ 18 = 1 remainder 5 |
| 3 | 18 ÷ 5 = 3 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 104 | 728 |
| 122 and 61 | 122 |
| 89 and 69 | 6141 |
| 185 and 144 | 26640 |
| 188 and 24 | 1128 |