Least Common Multiple (LCM) of 57 and 106
The least common multiple (LCM) of 57 and 106 is 6042.
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 106?
First, calculate the GCD of 57 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 106 = 0 remainder 57 |
| 2 | 106 ÷ 57 = 1 remainder 49 |
| 3 | 57 ÷ 49 = 1 remainder 8 |
| 4 | 49 ÷ 8 = 6 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 120 | 360 |
| 90 and 55 | 990 |
| 78 and 38 | 1482 |
| 138 and 119 | 16422 |
| 11 and 88 | 88 |