Least Common Multiple (LCM) of 191 and 120
The least common multiple (LCM) of 191 and 120 is 22920.
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 191 and 120?
First, calculate the GCD of 191 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 120 = 1 remainder 71 |
| 2 | 120 ÷ 71 = 1 remainder 49 |
| 3 | 71 ÷ 49 = 1 remainder 22 |
| 4 | 49 ÷ 22 = 2 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 113 | 11187 |
| 131 and 10 | 1310 |
| 142 and 47 | 6674 |
| 65 and 42 | 2730 |
| 52 and 138 | 3588 |