Least Common Multiple (LCM) of 102 and 57
The least common multiple (LCM) of 102 and 57 is 1938.
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 102 and 57?
First, calculate the GCD of 102 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 57 = 1 remainder 45 |
| 2 | 57 ÷ 45 = 1 remainder 12 |
| 3 | 45 ÷ 12 = 3 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 101 | 2121 |
| 191 and 88 | 16808 |
| 106 and 135 | 14310 |
| 10 and 137 | 1370 |
| 199 and 198 | 39402 |