Least Common Multiple (LCM) of 172 and 199
The least common multiple (LCM) of 172 and 199 is 34228.
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 172 and 199?
First, calculate the GCD of 172 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 199 = 0 remainder 172 |
| 2 | 199 ÷ 172 = 1 remainder 27 |
| 3 | 172 ÷ 27 = 6 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 54 | 2646 |
| 196 and 87 | 17052 |
| 60 and 50 | 300 |
| 200 and 170 | 3400 |
| 150 and 58 | 4350 |