Least Common Multiple (LCM) of 182 and 199
The least common multiple (LCM) of 182 and 199 is 36218.
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 182 and 199?
First, calculate the GCD of 182 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 182 ÷ 199 = 0 remainder 182 |
| 2 | 199 ÷ 182 = 1 remainder 17 |
| 3 | 182 ÷ 17 = 10 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 87 | 4176 |
| 90 and 141 | 4230 |
| 101 and 77 | 7777 |
| 174 and 108 | 3132 |
| 198 and 126 | 1386 |