Least Common Multiple (LCM) of 73 and 199
The least common multiple (LCM) of 73 and 199 is 14527.
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 73 and 199?
First, calculate the GCD of 73 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 199 = 0 remainder 73 |
| 2 | 199 ÷ 73 = 2 remainder 53 |
| 3 | 73 ÷ 53 = 1 remainder 20 |
| 4 | 53 ÷ 20 = 2 remainder 13 |
| 5 | 20 ÷ 13 = 1 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 146 | 9344 |
| 174 and 46 | 4002 |
| 51 and 162 | 2754 |
| 157 and 15 | 2355 |
| 125 and 141 | 17625 |