Least Common Multiple (LCM) of 135 and 109
The least common multiple (LCM) of 135 and 109 is 14715.
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 109?
First, calculate the GCD of 135 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 109 = 1 remainder 26 |
| 2 | 109 ÷ 26 = 4 remainder 5 |
| 3 | 26 ÷ 5 = 5 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 59 | 10325 |
| 172 and 98 | 8428 |
| 120 and 125 | 3000 |
| 99 and 149 | 14751 |
| 71 and 152 | 10792 |