Least Common Multiple (LCM) of 135 and 76
The least common multiple (LCM) of 135 and 76 is 10260.
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 76?
First, calculate the GCD of 135 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 76 = 1 remainder 59 |
| 2 | 76 ÷ 59 = 1 remainder 17 |
| 3 | 59 ÷ 17 = 3 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 60 | 1560 |
| 193 and 156 | 30108 |
| 180 and 169 | 30420 |
| 73 and 26 | 1898 |
| 187 and 198 | 3366 |