Least Common Multiple (LCM) of 124 and 105
The least common multiple (LCM) of 124 and 105 is 13020.
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 124 and 105?
First, calculate the GCD of 124 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 124 ÷ 105 = 1 remainder 19 |
| 2 | 105 ÷ 19 = 5 remainder 10 |
| 3 | 19 ÷ 10 = 1 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 187 | 20383 |
| 29 and 79 | 2291 |
| 186 and 86 | 7998 |
| 198 and 34 | 3366 |
| 172 and 134 | 11524 |