Least Common Multiple (LCM) of 57 and 105
The least common multiple (LCM) of 57 and 105 is 1995.
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 105?
First, calculate the GCD of 57 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 105 = 0 remainder 57 |
| 2 | 105 ÷ 57 = 1 remainder 48 |
| 3 | 57 ÷ 48 = 1 remainder 9 |
| 4 | 48 ÷ 9 = 5 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 45 | 1665 |
| 103 and 106 | 10918 |
| 15 and 135 | 135 |
| 72 and 68 | 1224 |
| 28 and 68 | 476 |