Least Common Multiple (LCM) of 160 and 199
The least common multiple (LCM) of 160 and 199 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 160 and 199?
First, calculate the GCD of 160 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 199 = 0 remainder 160 |
| 2 | 199 ÷ 160 = 1 remainder 39 |
| 3 | 160 ÷ 39 = 4 remainder 4 |
| 4 | 39 ÷ 4 = 9 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 152 | 2736 |
| 183 and 63 | 3843 |
| 165 and 104 | 17160 |
| 20 and 100 | 100 |
| 134 and 184 | 12328 |