Least Common Multiple (LCM) of 23 and 31
The least common multiple (LCM) of 23 and 31 is 713.
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 31?
First, calculate the GCD of 23 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 31 = 0 remainder 23 |
| 2 | 31 ÷ 23 = 1 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 103 | 17922 |
| 17 and 103 | 1751 |
| 80 and 164 | 3280 |
| 37 and 199 | 7363 |
| 180 and 47 | 8460 |