Least Common Multiple (LCM) of 57 and 159
The least common multiple (LCM) of 57 and 159 is 3021.
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 159?
First, calculate the GCD of 57 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 159 = 0 remainder 57 |
| 2 | 159 ÷ 57 = 2 remainder 45 |
| 3 | 57 ÷ 45 = 1 remainder 12 |
| 4 | 45 ÷ 12 = 3 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 107 | 8346 |
| 173 and 39 | 6747 |
| 114 and 55 | 6270 |
| 169 and 124 | 20956 |
| 56 and 61 | 3416 |