Least Common Multiple (LCM) of 124 and 135
The least common multiple (LCM) of 124 and 135 is 16740.
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 135?
First, calculate the GCD of 124 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 124 ÷ 135 = 0 remainder 124 |
| 2 | 135 ÷ 124 = 1 remainder 11 |
| 3 | 124 ÷ 11 = 11 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 76 | 76 |
| 125 and 30 | 750 |
| 108 and 124 | 3348 |
| 15 and 54 | 270 |
| 162 and 29 | 4698 |