Least Common Multiple (LCM) of 57 and 164
The least common multiple (LCM) of 57 and 164 is 9348.
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 164?
First, calculate the GCD of 57 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 164 = 0 remainder 57 |
| 2 | 164 ÷ 57 = 2 remainder 50 |
| 3 | 57 ÷ 50 = 1 remainder 7 |
| 4 | 50 ÷ 7 = 7 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 114 | 5700 |
| 97 and 109 | 10573 |
| 116 and 60 | 1740 |
| 159 and 173 | 27507 |
| 111 and 155 | 17205 |