Least Common Multiple (LCM) of 31 and 13
The least common multiple (LCM) of 31 and 13 is 403.
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 13?
First, calculate the GCD of 31 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 13 = 2 remainder 5 |
| 2 | 13 ÷ 5 = 2 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 14 | 966 |
| 185 and 102 | 18870 |
| 52 and 153 | 7956 |
| 45 and 144 | 720 |
| 133 and 61 | 8113 |