Least Common Multiple (LCM) of 76 and 135
The least common multiple (LCM) of 76 and 135 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 76 and 135?
First, calculate the GCD of 76 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 135 = 0 remainder 76 |
| 2 | 135 ÷ 76 = 1 remainder 59 |
| 3 | 76 ÷ 59 = 1 remainder 17 |
| 4 | 59 ÷ 17 = 3 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 59 | 8024 |
| 18 and 99 | 198 |
| 63 and 80 | 5040 |
| 89 and 59 | 5251 |
| 180 and 173 | 31140 |