Least Common Multiple (LCM) of 117 and 191
The least common multiple (LCM) of 117 and 191 is 22347.
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 191?
First, calculate the GCD of 117 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 191 = 0 remainder 117 |
| 2 | 191 ÷ 117 = 1 remainder 74 |
| 3 | 117 ÷ 74 = 1 remainder 43 |
| 4 | 74 ÷ 43 = 1 remainder 31 |
| 5 | 43 ÷ 31 = 1 remainder 12 |
| 6 | 31 ÷ 12 = 2 remainder 7 |
| 7 | 12 ÷ 7 = 1 remainder 5 |
| 8 | 7 ÷ 5 = 1 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 190 | 10070 |
| 76 and 113 | 8588 |
| 73 and 38 | 2774 |
| 159 and 75 | 3975 |
| 138 and 149 | 20562 |