Least Common Multiple (LCM) of 107 and 124
The least common multiple (LCM) of 107 and 124 is 13268.
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 107 and 124?
First, calculate the GCD of 107 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 124 = 0 remainder 107 |
| 2 | 124 ÷ 107 = 1 remainder 17 |
| 3 | 107 ÷ 17 = 6 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 13 | 13 |
| 127 and 33 | 4191 |
| 54 and 182 | 4914 |
| 199 and 79 | 15721 |
| 45 and 195 | 585 |