Least Common Multiple (LCM) of 57 and 119
The least common multiple (LCM) of 57 and 119 is 6783.
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 119?
First, calculate the GCD of 57 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 119 = 0 remainder 57 |
| 2 | 119 ÷ 57 = 2 remainder 5 |
| 3 | 57 ÷ 5 = 11 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 128 | 6016 |
| 14 and 120 | 840 |
| 105 and 126 | 630 |
| 38 and 173 | 6574 |
| 95 and 101 | 9595 |