Least Common Multiple (LCM) of 51 and 199
The least common multiple (LCM) of 51 and 199 is 10149.
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 199?
First, calculate the GCD of 51 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 199 = 0 remainder 51 |
| 2 | 199 ÷ 51 = 3 remainder 46 |
| 3 | 51 ÷ 46 = 1 remainder 5 |
| 4 | 46 ÷ 5 = 9 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 176 | 19184 |
| 38 and 10 | 190 |
| 49 and 113 | 5537 |
| 138 and 50 | 3450 |
| 14 and 156 | 1092 |