Least Common Multiple (LCM) of 51 and 198
The least common multiple (LCM) of 51 and 198 is 3366.
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 51 and 198?
First, calculate the GCD of 51 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 198 = 0 remainder 51 |
| 2 | 198 ÷ 51 = 3 remainder 45 |
| 3 | 51 ÷ 45 = 1 remainder 6 |
| 4 | 45 ÷ 6 = 7 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 121 | 24200 |
| 142 and 47 | 6674 |
| 190 and 22 | 2090 |
| 155 and 119 | 18445 |
| 137 and 57 | 7809 |