Least Common Multiple (LCM) of 31 and 135
The least common multiple (LCM) of 31 and 135 is 4185.
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 135?
First, calculate the GCD of 31 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 135 = 0 remainder 31 |
| 2 | 135 ÷ 31 = 4 remainder 11 |
| 3 | 31 ÷ 11 = 2 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 124 | 16244 |
| 108 and 165 | 5940 |
| 104 and 186 | 9672 |
| 86 and 131 | 11266 |
| 25 and 111 | 2775 |