Least Common Multiple (LCM) of 77 and 199
The least common multiple (LCM) of 77 and 199 is 15323.
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 77 and 199?
First, calculate the GCD of 77 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 199 = 0 remainder 77 |
| 2 | 199 ÷ 77 = 2 remainder 45 |
| 3 | 77 ÷ 45 = 1 remainder 32 |
| 4 | 45 ÷ 32 = 1 remainder 13 |
| 5 | 32 ÷ 13 = 2 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 81 | 8829 |
| 56 and 24 | 168 |
| 173 and 86 | 14878 |
| 61 and 173 | 10553 |
| 55 and 142 | 7810 |