Least Common Multiple (LCM) of 106 and 135
The least common multiple (LCM) of 106 and 135 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 106 and 135?
First, calculate the GCD of 106 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 135 = 0 remainder 106 |
| 2 | 135 ÷ 106 = 1 remainder 29 |
| 3 | 106 ÷ 29 = 3 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 144 | 3600 |
| 133 and 58 | 7714 |
| 56 and 98 | 392 |
| 90 and 140 | 1260 |
| 29 and 141 | 4089 |