Least Common Multiple (LCM) of 54 and 199
The least common multiple (LCM) of 54 and 199 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 54 and 199?
First, calculate the GCD of 54 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 199 = 0 remainder 54 |
| 2 | 199 ÷ 54 = 3 remainder 37 |
| 3 | 54 ÷ 37 = 1 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 63 | 4221 |
| 12 and 100 | 300 |
| 160 and 27 | 4320 |
| 166 and 104 | 8632 |
| 35 and 15 | 105 |