Least Common Multiple (LCM) of 123 and 31
The least common multiple (LCM) of 123 and 31 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 123 and 31?
First, calculate the GCD of 123 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 31 = 3 remainder 30 |
| 2 | 31 ÷ 30 = 1 remainder 1 |
| 3 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 117 | 12519 |
| 63 and 124 | 7812 |
| 177 and 101 | 17877 |
| 153 and 30 | 1530 |
| 180 and 145 | 5220 |