Least Common Multiple (LCM) of 57 and 49
The least common multiple (LCM) of 57 and 49 is 2793.
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 49?
First, calculate the GCD of 57 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 49 = 1 remainder 8 |
| 2 | 49 ÷ 8 = 6 remainder 1 |
| 3 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 180 | 180 |
| 40 and 128 | 640 |
| 147 and 200 | 29400 |
| 169 and 52 | 676 |
| 112 and 55 | 6160 |