Least Common Multiple (LCM) of 13 and 57
The least common multiple (LCM) of 13 and 57 is 741.
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 13 and 57?
First, calculate the GCD of 13 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 57 = 0 remainder 13 |
| 2 | 57 ÷ 13 = 4 remainder 5 |
| 3 | 13 ÷ 5 = 2 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 90 | 1170 |
| 142 and 36 | 2556 |
| 194 and 76 | 7372 |
| 176 and 122 | 10736 |
| 199 and 15 | 2985 |