Least Common Multiple (LCM) of 31 and 23
The least common multiple (LCM) of 31 and 23 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 31 and 23?
First, calculate the GCD of 31 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 23 = 1 remainder 8 |
| 2 | 23 ÷ 8 = 2 remainder 7 |
| 3 | 8 ÷ 7 = 1 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 42 | 1428 |
| 198 and 194 | 19206 |
| 100 and 157 | 15700 |
| 165 and 141 | 7755 |
| 11 and 47 | 517 |