Least Common Multiple (LCM) of 109 and 135
The least common multiple (LCM) of 109 and 135 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 109 and 135?
First, calculate the GCD of 109 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 135 = 0 remainder 109 |
| 2 | 135 ÷ 109 = 1 remainder 26 |
| 3 | 109 ÷ 26 = 4 remainder 5 |
| 4 | 26 ÷ 5 = 5 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 74 | 14430 |
| 59 and 15 | 885 |
| 35 and 120 | 840 |
| 186 and 60 | 1860 |
| 165 and 23 | 3795 |