Least Common Multiple (LCM) of 193 and 76
The least common multiple (LCM) of 193 and 76 is 14668.
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 76?
First, calculate the GCD of 193 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 76 = 2 remainder 41 |
| 2 | 76 ÷ 41 = 1 remainder 35 |
| 3 | 41 ÷ 35 = 1 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 149 | 2235 |
| 176 and 21 | 3696 |
| 174 and 181 | 31494 |
| 74 and 96 | 3552 |
| 36 and 51 | 612 |