Least Common Multiple (LCM) of 23 and 114
The least common multiple (LCM) of 23 and 114 is 2622.
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 23 and 114?
First, calculate the GCD of 23 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 114 = 0 remainder 23 |
| 2 | 114 ÷ 23 = 4 remainder 22 |
| 3 | 23 ÷ 22 = 1 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 42 | 8106 |
| 181 and 116 | 20996 |
| 145 and 169 | 24505 |
| 98 and 162 | 7938 |
| 18 and 142 | 1278 |