Least Common Multiple (LCM) of 57 and 135
The least common multiple (LCM) of 57 and 135 is 2565.
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 57 and 135?
First, calculate the GCD of 57 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 135 = 0 remainder 57 |
| 2 | 135 ÷ 57 = 2 remainder 21 |
| 3 | 57 ÷ 21 = 2 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 65 | 1040 |
| 195 and 97 | 18915 |
| 110 and 182 | 10010 |
| 123 and 66 | 2706 |
| 148 and 94 | 6956 |