Least Common Multiple (LCM) of 135 and 122
The least common multiple (LCM) of 135 and 122 is 16470.
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 135 and 122?
First, calculate the GCD of 135 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 122 = 1 remainder 13 |
| 2 | 122 ÷ 13 = 9 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 174 | 6090 |
| 105 and 99 | 3465 |
| 132 and 97 | 12804 |
| 83 and 82 | 6806 |
| 182 and 20 | 1820 |