Least Common Multiple (LCM) of 31 and 69
The least common multiple (LCM) of 31 and 69 is 2139.
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 69?
First, calculate the GCD of 31 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 69 = 0 remainder 31 |
| 2 | 69 ÷ 31 = 2 remainder 7 |
| 3 | 31 ÷ 7 = 4 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 18 | 1098 |
| 110 and 59 | 6490 |
| 145 and 185 | 5365 |
| 134 and 167 | 22378 |
| 129 and 188 | 24252 |