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 |
|---|---|
| 195 and 42 | 2730 |
| 52 and 114 | 2964 |
| 140 and 40 | 280 |
| 114 and 93 | 3534 |
| 188 and 154 | 14476 |