Least Common Multiple (LCM) of 30 and 197
The least common multiple (LCM) of 30 and 197 is 5910.
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 197?
First, calculate the GCD of 30 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 197 = 0 remainder 30 |
| 2 | 197 ÷ 30 = 6 remainder 17 |
| 3 | 30 ÷ 17 = 1 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 112 | 9072 |
| 88 and 10 | 440 |
| 37 and 99 | 3663 |
| 99 and 65 | 6435 |
| 125 and 12 | 1500 |