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 |
|---|---|
| 200 and 158 | 15800 |
| 174 and 76 | 6612 |
| 67 and 63 | 4221 |
| 47 and 162 | 7614 |
| 96 and 164 | 3936 |