Least Common Multiple (LCM) of 117 and 199
The least common multiple (LCM) of 117 and 199 is 23283.
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 117 and 199?
First, calculate the GCD of 117 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 199 = 0 remainder 117 |
| 2 | 199 ÷ 117 = 1 remainder 82 |
| 3 | 117 ÷ 82 = 1 remainder 35 |
| 4 | 82 ÷ 35 = 2 remainder 12 |
| 5 | 35 ÷ 12 = 2 remainder 11 |
| 6 | 12 ÷ 11 = 1 remainder 1 |
| 7 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 190 | 16340 |
| 160 and 50 | 800 |
| 175 and 42 | 1050 |
| 134 and 175 | 23450 |
| 67 and 138 | 9246 |