Least Common Multiple (LCM) of 51 and 180
The least common multiple (LCM) of 51 and 180 is 3060.
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 180?
First, calculate the GCD of 51 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 180 = 0 remainder 51 |
| 2 | 180 ÷ 51 = 3 remainder 27 |
| 3 | 51 ÷ 27 = 1 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 43 | 8213 |
| 190 and 200 | 3800 |
| 198 and 68 | 6732 |
| 41 and 143 | 5863 |
| 120 and 145 | 3480 |