Least Common Multiple (LCM) of 57 and 134
The least common multiple (LCM) of 57 and 134 is 7638.
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 134?
First, calculate the GCD of 57 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 134 = 0 remainder 57 |
| 2 | 134 ÷ 57 = 2 remainder 20 |
| 3 | 57 ÷ 20 = 2 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 154 | 2310 |
| 110 and 16 | 880 |
| 108 and 57 | 2052 |
| 133 and 91 | 1729 |
| 36 and 79 | 2844 |