Least Common Multiple (LCM) of 122 and 75
The least common multiple (LCM) of 122 and 75 is 9150.
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 122 and 75?
First, calculate the GCD of 122 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 75 = 1 remainder 47 |
| 2 | 75 ÷ 47 = 1 remainder 28 |
| 3 | 47 ÷ 28 = 1 remainder 19 |
| 4 | 28 ÷ 19 = 1 remainder 9 |
| 5 | 19 ÷ 9 = 2 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 41 | 3649 |
| 140 and 77 | 1540 |
| 46 and 117 | 5382 |
| 126 and 41 | 5166 |
| 186 and 189 | 11718 |