Least Common Multiple (LCM) of 21 and 82
The least common multiple (LCM) of 21 and 82 is 1722.
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 82?
First, calculate the GCD of 21 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 82 = 0 remainder 21 |
| 2 | 82 ÷ 21 = 3 remainder 19 |
| 3 | 21 ÷ 19 = 1 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 115 | 11615 |
| 47 and 17 | 799 |
| 117 and 10 | 1170 |
| 45 and 123 | 1845 |
| 21 and 67 | 1407 |