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 |
|---|---|
| 107 and 42 | 4494 |
| 107 and 30 | 3210 |
| 37 and 78 | 2886 |
| 38 and 122 | 2318 |
| 56 and 30 | 840 |