Least Common Multiple (LCM) of 114 and 23
The least common multiple (LCM) of 114 and 23 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 114 and 23?
First, calculate the GCD of 114 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 23 = 4 remainder 22 |
| 2 | 23 ÷ 22 = 1 remainder 1 |
| 3 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 23 | 2553 |
| 10 and 41 | 410 |
| 136 and 160 | 2720 |
| 82 and 47 | 3854 |
| 22 and 194 | 2134 |