Least Common Multiple (LCM) of 21 and 180
The least common multiple (LCM) of 21 and 180 is 1260.
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 21 and 180?
First, calculate the GCD of 21 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 180 = 0 remainder 21 |
| 2 | 180 ÷ 21 = 8 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 80 | 720 |
| 122 and 60 | 3660 |
| 133 and 149 | 19817 |
| 57 and 135 | 2565 |
| 59 and 199 | 11741 |