Least Common Multiple (LCM) of 197 and 51
The least common multiple (LCM) of 197 and 51 is 10047.
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 197 and 51?
First, calculate the GCD of 197 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 51 = 3 remainder 44 |
| 2 | 51 ÷ 44 = 1 remainder 7 |
| 3 | 44 ÷ 7 = 6 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 104 | 1144 |
| 124 and 21 | 2604 |
| 84 and 143 | 12012 |
| 43 and 164 | 7052 |
| 100 and 171 | 17100 |