Least Common Multiple (LCM) of 120 and 191
The least common multiple (LCM) of 120 and 191 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 120 and 191?
First, calculate the GCD of 120 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 191 = 0 remainder 120 |
| 2 | 191 ÷ 120 = 1 remainder 71 |
| 3 | 120 ÷ 71 = 1 remainder 49 |
| 4 | 71 ÷ 49 = 1 remainder 22 |
| 5 | 49 ÷ 22 = 2 remainder 5 |
| 6 | 22 ÷ 5 = 4 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 37 | 7030 |
| 128 and 170 | 10880 |
| 20 and 118 | 1180 |
| 154 and 115 | 17710 |
| 150 and 118 | 8850 |