Least Common Multiple (LCM) of 23 and 113
The least common multiple (LCM) of 23 and 113 is 2599.
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 113?
First, calculate the GCD of 23 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 113 = 0 remainder 23 |
| 2 | 113 ÷ 23 = 4 remainder 21 |
| 3 | 23 ÷ 21 = 1 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 100 | 3700 |
| 145 and 53 | 7685 |
| 64 and 21 | 1344 |
| 163 and 131 | 21353 |
| 67 and 135 | 9045 |