Least Common Multiple (LCM) of 57 and 160
The least common multiple (LCM) of 57 and 160 is 9120.
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 160?
First, calculate the GCD of 57 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 160 = 0 remainder 57 |
| 2 | 160 ÷ 57 = 2 remainder 46 |
| 3 | 57 ÷ 46 = 1 remainder 11 |
| 4 | 46 ÷ 11 = 4 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 173 | 20760 |
| 11 and 146 | 1606 |
| 32 and 12 | 96 |
| 108 and 178 | 9612 |
| 100 and 142 | 7100 |