Least Common Multiple (LCM) of 199 and 160
The least common multiple (LCM) of 199 and 160 is 31840.
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 199 and 160?
First, calculate the GCD of 199 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 160 = 1 remainder 39 |
| 2 | 160 ÷ 39 = 4 remainder 4 |
| 3 | 39 ÷ 4 = 9 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 42 | 1554 |
| 180 and 168 | 2520 |
| 25 and 62 | 1550 |
| 155 and 63 | 9765 |
| 133 and 57 | 399 |