Least Common Multiple (LCM) of 135 and 87
The least common multiple (LCM) of 135 and 87 is 3915.
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 87?
First, calculate the GCD of 135 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 87 = 1 remainder 48 |
| 2 | 87 ÷ 48 = 1 remainder 39 |
| 3 | 48 ÷ 39 = 1 remainder 9 |
| 4 | 39 ÷ 9 = 4 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 19 | 779 |
| 55 and 31 | 1705 |
| 60 and 174 | 1740 |
| 90 and 16 | 720 |
| 198 and 51 | 3366 |