Least Common Multiple (LCM) of 57 and 113
The least common multiple (LCM) of 57 and 113 is 6441.
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 113?
First, calculate the GCD of 57 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 113 = 0 remainder 57 |
| 2 | 113 ÷ 57 = 1 remainder 56 |
| 3 | 57 ÷ 56 = 1 remainder 1 |
| 4 | 56 ÷ 1 = 56 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 95 | 3420 |
| 88 and 149 | 13112 |
| 113 and 97 | 10961 |
| 57 and 176 | 10032 |
| 105 and 191 | 20055 |