Least Common Multiple (LCM) of 51 and 193
The least common multiple (LCM) of 51 and 193 is 9843.
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 51 and 193?
First, calculate the GCD of 51 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 193 = 0 remainder 51 |
| 2 | 193 ÷ 51 = 3 remainder 40 |
| 3 | 51 ÷ 40 = 1 remainder 11 |
| 4 | 40 ÷ 11 = 3 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 131 | 19388 |
| 160 and 78 | 6240 |
| 120 and 89 | 10680 |
| 157 and 20 | 3140 |
| 143 and 87 | 12441 |