Least Common Multiple (LCM) of 31 and 14
The least common multiple (LCM) of 31 and 14 is 434.
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 14?
First, calculate the GCD of 31 and 14 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 14 = 2 remainder 3 |
| 2 | 14 ÷ 3 = 4 remainder 2 |
| 3 | 3 ÷ 2 = 1 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 123 | 8364 |
| 114 and 97 | 11058 |
| 132 and 45 | 1980 |
| 180 and 160 | 1440 |
| 151 and 176 | 26576 |