Least Common Multiple (LCM) of 30 and 193
The least common multiple (LCM) of 30 and 193 is 5790.
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 193?
First, calculate the GCD of 30 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 193 = 0 remainder 30 |
| 2 | 193 ÷ 30 = 6 remainder 13 |
| 3 | 30 ÷ 13 = 2 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 170 | 8160 |
| 112 and 52 | 1456 |
| 120 and 86 | 5160 |
| 32 and 111 | 3552 |
| 115 and 152 | 17480 |