Least Common Multiple (LCM) of 27 and 199
The least common multiple (LCM) of 27 and 199 is 5373.
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 27 and 199?
First, calculate the GCD of 27 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 199 = 0 remainder 27 |
| 2 | 199 ÷ 27 = 7 remainder 10 |
| 3 | 27 ÷ 10 = 2 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 69 | 11730 |
| 131 and 71 | 9301 |
| 182 and 165 | 30030 |
| 156 and 144 | 1872 |
| 138 and 133 | 18354 |