Least Common Multiple (LCM) of 31 and 39
The least common multiple (LCM) of 31 and 39 is 1209.
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 39?
First, calculate the GCD of 31 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 39 = 0 remainder 31 |
| 2 | 39 ÷ 31 = 1 remainder 8 |
| 3 | 31 ÷ 8 = 3 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 192 | 13632 |
| 14 and 188 | 1316 |
| 49 and 106 | 5194 |
| 126 and 31 | 3906 |
| 125 and 132 | 16500 |