Least Common Multiple (LCM) of 57 and 114
The least common multiple (LCM) of 57 and 114 is 114.
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 114?
First, calculate the GCD of 57 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 114 = 0 remainder 57 |
| 2 | 114 ÷ 57 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 73 | 12921 |
| 196 and 140 | 980 |
| 196 and 164 | 8036 |
| 157 and 150 | 23550 |
| 21 and 195 | 1365 |