Least Common Multiple (LCM) of 135 and 77
The least common multiple (LCM) of 135 and 77 is 10395.
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 77?
First, calculate the GCD of 135 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 77 = 1 remainder 58 |
| 2 | 77 ÷ 58 = 1 remainder 19 |
| 3 | 58 ÷ 19 = 3 remainder 1 |
| 4 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 41 | 1435 |
| 60 and 191 | 11460 |
| 199 and 169 | 33631 |
| 15 and 136 | 2040 |
| 187 and 34 | 374 |