Least Common Multiple (LCM) of 199 and 54
The least common multiple (LCM) of 199 and 54 is 10746.
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 199 and 54?
First, calculate the GCD of 199 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 54 = 3 remainder 37 |
| 2 | 54 ÷ 37 = 1 remainder 17 |
| 3 | 37 ÷ 17 = 2 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 14 | 2086 |
| 113 and 34 | 3842 |
| 137 and 73 | 10001 |
| 62 and 174 | 5394 |
| 173 and 79 | 13667 |