Least Common Multiple (LCM) of 193 and 75
The least common multiple (LCM) of 193 and 75 is 14475.
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 193 and 75?
First, calculate the GCD of 193 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 75 = 2 remainder 43 |
| 2 | 75 ÷ 43 = 1 remainder 32 |
| 3 | 43 ÷ 32 = 1 remainder 11 |
| 4 | 32 ÷ 11 = 2 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 20 | 1780 |
| 152 and 120 | 2280 |
| 117 and 120 | 4680 |
| 14 and 91 | 182 |
| 124 and 40 | 1240 |