Least Common Multiple (LCM) of 21 and 80
The least common multiple (LCM) of 21 and 80 is 1680.
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 80?
First, calculate the GCD of 21 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 80 = 0 remainder 21 |
| 2 | 80 ÷ 21 = 3 remainder 17 |
| 3 | 21 ÷ 17 = 1 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 65 | 4355 |
| 90 and 125 | 2250 |
| 138 and 63 | 2898 |
| 130 and 187 | 24310 |
| 199 and 170 | 33830 |