Least Common Multiple (LCM) of 122 and 140
The least common multiple (LCM) of 122 and 140 is 8540.
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 140?
First, calculate the GCD of 122 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 140 = 0 remainder 122 |
| 2 | 140 ÷ 122 = 1 remainder 18 |
| 3 | 122 ÷ 18 = 6 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 165 | 495 |
| 50 and 183 | 9150 |
| 64 and 150 | 4800 |
| 67 and 112 | 7504 |
| 70 and 111 | 7770 |