Least Common Multiple (LCM) of 135 and 106
The least common multiple (LCM) of 135 and 106 is 14310.
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 106?
First, calculate the GCD of 135 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 106 = 1 remainder 29 |
| 2 | 106 ÷ 29 = 3 remainder 19 |
| 3 | 29 ÷ 19 = 1 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 12 | 2100 |
| 181 and 180 | 32580 |
| 199 and 195 | 38805 |
| 66 and 18 | 198 |
| 144 and 20 | 720 |