Least Common Multiple (LCM) of 80 and 21
The least common multiple (LCM) of 80 and 21 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 80 and 21?
First, calculate the GCD of 80 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 21 = 3 remainder 17 |
| 2 | 21 ÷ 17 = 1 remainder 4 |
| 3 | 17 ÷ 4 = 4 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 140 | 4340 |
| 68 and 179 | 12172 |
| 188 and 61 | 11468 |
| 191 and 103 | 19673 |
| 116 and 83 | 9628 |