Least Common Multiple (LCM) of 30 and 199
The least common multiple (LCM) of 30 and 199 is 5970.
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 199?
First, calculate the GCD of 30 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 199 = 0 remainder 30 |
| 2 | 199 ÷ 30 = 6 remainder 19 |
| 3 | 30 ÷ 19 = 1 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 171 | 19836 |
| 143 and 71 | 10153 |
| 165 and 104 | 17160 |
| 96 and 130 | 6240 |
| 53 and 16 | 848 |