Least Common Multiple (LCM) of 30 and 191
The least common multiple (LCM) of 30 and 191 is 5730.
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 30 and 191?
First, calculate the GCD of 30 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 191 = 0 remainder 30 |
| 2 | 191 ÷ 30 = 6 remainder 11 |
| 3 | 30 ÷ 11 = 2 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 42 | 7014 |
| 97 and 33 | 3201 |
| 145 and 187 | 27115 |
| 97 and 10 | 970 |
| 198 and 137 | 27126 |