Least Common Multiple (LCM) of 57 and 138
The least common multiple (LCM) of 57 and 138 is 2622.
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 138?
First, calculate the GCD of 57 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 138 = 0 remainder 57 |
| 2 | 138 ÷ 57 = 2 remainder 24 |
| 3 | 57 ÷ 24 = 2 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 42 | 84 |
| 134 and 37 | 4958 |
| 76 and 165 | 12540 |
| 76 and 125 | 9500 |
| 77 and 115 | 8855 |