Least Common Multiple (LCM) of 31 and 138
The least common multiple (LCM) of 31 and 138 is 4278.
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 138?
First, calculate the GCD of 31 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 138 = 0 remainder 31 |
| 2 | 138 ÷ 31 = 4 remainder 14 |
| 3 | 31 ÷ 14 = 2 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 19 | 2299 |
| 161 and 161 | 161 |
| 195 and 13 | 195 |
| 32 and 144 | 288 |
| 45 and 181 | 8145 |