Least Common Multiple (LCM) of 116 and 199
The least common multiple (LCM) of 116 and 199 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 116 and 199?
First, calculate the GCD of 116 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 199 = 0 remainder 116 |
| 2 | 199 ÷ 116 = 1 remainder 83 |
| 3 | 116 ÷ 83 = 1 remainder 33 |
| 4 | 83 ÷ 33 = 2 remainder 17 |
| 5 | 33 ÷ 17 = 1 remainder 16 |
| 6 | 17 ÷ 16 = 1 remainder 1 |
| 7 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 70 | 1190 |
| 137 and 102 | 13974 |
| 178 and 51 | 9078 |
| 124 and 140 | 4340 |
| 109 and 55 | 5995 |