Least Common Multiple (LCM) of 57 and 91
The least common multiple (LCM) of 57 and 91 is 5187.
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 91?
First, calculate the GCD of 57 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 91 = 0 remainder 57 |
| 2 | 91 ÷ 57 = 1 remainder 34 |
| 3 | 57 ÷ 34 = 1 remainder 23 |
| 4 | 34 ÷ 23 = 1 remainder 11 |
| 5 | 23 ÷ 11 = 2 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 27 | 3051 |
| 156 and 198 | 5148 |
| 21 and 77 | 231 |
| 145 and 187 | 27115 |
| 127 and 91 | 11557 |