Least Common Multiple (LCM) of 57 and 139
The least common multiple (LCM) of 57 and 139 is 7923.
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 139?
First, calculate the GCD of 57 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 139 = 0 remainder 57 |
| 2 | 139 ÷ 57 = 2 remainder 25 |
| 3 | 57 ÷ 25 = 2 remainder 7 |
| 4 | 25 ÷ 7 = 3 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 128 | 1920 |
| 39 and 28 | 1092 |
| 197 and 35 | 6895 |
| 93 and 81 | 2511 |
| 16 and 190 | 1520 |