Least Common Multiple (LCM) of 117 and 190
The least common multiple (LCM) of 117 and 190 is 22230.
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 190?
First, calculate the GCD of 117 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 190 = 0 remainder 117 |
| 2 | 190 ÷ 117 = 1 remainder 73 |
| 3 | 117 ÷ 73 = 1 remainder 44 |
| 4 | 73 ÷ 44 = 1 remainder 29 |
| 5 | 44 ÷ 29 = 1 remainder 15 |
| 6 | 29 ÷ 15 = 1 remainder 14 |
| 7 | 15 ÷ 14 = 1 remainder 1 |
| 8 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 196 | 6468 |
| 174 and 10 | 870 |
| 195 and 125 | 4875 |
| 86 and 20 | 860 |
| 67 and 48 | 3216 |