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 |
|---|---|
| 75 and 133 | 9975 |
| 52 and 111 | 5772 |
| 56 and 188 | 2632 |
| 138 and 150 | 3450 |
| 180 and 90 | 180 |