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 |
|---|---|
| 13 and 98 | 1274 |
| 163 and 157 | 25591 |
| 138 and 89 | 12282 |
| 200 and 86 | 8600 |
| 145 and 166 | 24070 |