Least Common Multiple (LCM) of 199 and 68
The least common multiple (LCM) of 199 and 68 is 13532.
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 68?
First, calculate the GCD of 199 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 68 = 2 remainder 63 |
| 2 | 68 ÷ 63 = 1 remainder 5 |
| 3 | 63 ÷ 5 = 12 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 150 | 3150 |
| 110 and 62 | 3410 |
| 103 and 161 | 16583 |
| 192 and 37 | 7104 |
| 164 and 138 | 11316 |