Least Common Multiple (LCM) of 51 and 164
The least common multiple (LCM) of 51 and 164 is 8364.
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 164?
First, calculate the GCD of 51 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 164 = 0 remainder 51 |
| 2 | 164 ÷ 51 = 3 remainder 11 |
| 3 | 51 ÷ 11 = 4 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 51 | 3366 |
| 18 and 187 | 3366 |
| 182 and 188 | 17108 |
| 38 and 181 | 6878 |
| 154 and 90 | 6930 |