Least Common Multiple (LCM) of 123 and 75
The least common multiple (LCM) of 123 and 75 is 3075.
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 75?
First, calculate the GCD of 123 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 75 = 1 remainder 48 |
| 2 | 75 ÷ 48 = 1 remainder 27 |
| 3 | 48 ÷ 27 = 1 remainder 21 |
| 4 | 27 ÷ 21 = 1 remainder 6 |
| 5 | 21 ÷ 6 = 3 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 102 | 408 |
| 104 and 200 | 2600 |
| 182 and 83 | 15106 |
| 32 and 180 | 1440 |
| 21 and 59 | 1239 |