Least Common Multiple (LCM) of 135 and 107
The least common multiple (LCM) of 135 and 107 is 14445.
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 107?
First, calculate the GCD of 135 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 107 = 1 remainder 28 |
| 2 | 107 ÷ 28 = 3 remainder 23 |
| 3 | 28 ÷ 23 = 1 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 35 | 560 |
| 18 and 186 | 558 |
| 162 and 141 | 7614 |
| 34 and 33 | 1122 |
| 108 and 28 | 756 |