Least Common Multiple (LCM) of 31 and 114
The least common multiple (LCM) of 31 and 114 is 3534.
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 114?
First, calculate the GCD of 31 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 114 = 0 remainder 31 |
| 2 | 114 ÷ 31 = 3 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 79 | 14220 |
| 139 and 120 | 16680 |
| 115 and 14 | 1610 |
| 125 and 60 | 1500 |
| 195 and 30 | 390 |