Least Common Multiple (LCM) of 31 and 123
The least common multiple (LCM) of 31 and 123 is 3813.
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 123?
First, calculate the GCD of 31 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 123 = 0 remainder 31 |
| 2 | 123 ÷ 31 = 3 remainder 30 |
| 3 | 31 ÷ 30 = 1 remainder 1 |
| 4 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 66 | 132 |
| 117 and 21 | 819 |
| 22 and 82 | 902 |
| 182 and 192 | 17472 |
| 58 and 147 | 8526 |