Least Common Multiple (LCM) of 199 and 63
The least common multiple (LCM) of 199 and 63 is 12537.
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 63?
First, calculate the GCD of 199 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 63 = 3 remainder 10 |
| 2 | 63 ÷ 10 = 6 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 132 | 4884 |
| 71 and 77 | 5467 |
| 95 and 85 | 1615 |
| 100 and 177 | 17700 |
| 121 and 55 | 605 |