Least Common Multiple (LCM) of 199 and 116
The least common multiple (LCM) of 199 and 116 is 23084.
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 116?
First, calculate the GCD of 199 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 116 = 1 remainder 83 |
| 2 | 116 ÷ 83 = 1 remainder 33 |
| 3 | 83 ÷ 33 = 2 remainder 17 |
| 4 | 33 ÷ 17 = 1 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 136 | 8840 |
| 95 and 112 | 10640 |
| 106 and 15 | 1590 |
| 187 and 101 | 18887 |
| 32 and 21 | 672 |