Least Common Multiple (LCM) of 57 and 162
The least common multiple (LCM) of 57 and 162 is 3078.
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 162?
First, calculate the GCD of 57 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 162 = 0 remainder 57 |
| 2 | 162 ÷ 57 = 2 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 |
|---|---|
| 139 and 95 | 13205 |
| 104 and 189 | 19656 |
| 30 and 82 | 1230 |
| 36 and 68 | 612 |
| 188 and 75 | 14100 |