Least Common Multiple (LCM) of 31 and 134
The least common multiple (LCM) of 31 and 134 is 4154.
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 134?
First, calculate the GCD of 31 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 134 = 0 remainder 31 |
| 2 | 134 ÷ 31 = 4 remainder 10 |
| 3 | 31 ÷ 10 = 3 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 32 | 1184 |
| 176 and 20 | 880 |
| 61 and 143 | 8723 |
| 121 and 189 | 22869 |
| 195 and 129 | 8385 |