Least Common Multiple (LCM) of 23 and 115
The least common multiple (LCM) of 23 and 115 is 115.
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 115?
First, calculate the GCD of 23 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 115 = 0 remainder 23 |
| 2 | 115 ÷ 23 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 82 | 246 |
| 58 and 100 | 2900 |
| 120 and 109 | 13080 |
| 100 and 170 | 1700 |
| 98 and 108 | 5292 |