Least Common Multiple (LCM) of 34 and 57
The least common multiple (LCM) of 34 and 57 is 1938.
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 34 and 57?
First, calculate the GCD of 34 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 57 = 0 remainder 34 |
| 2 | 57 ÷ 34 = 1 remainder 23 |
| 3 | 34 ÷ 23 = 1 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 55 | 660 |
| 67 and 117 | 7839 |
| 37 and 200 | 7400 |
| 179 and 171 | 30609 |
| 148 and 40 | 1480 |