Least Common Multiple (LCM) of 21 and 83
The least common multiple (LCM) of 21 and 83 is 1743.
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 83?
First, calculate the GCD of 21 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 83 = 0 remainder 21 |
| 2 | 83 ÷ 21 = 3 remainder 20 |
| 3 | 21 ÷ 20 = 1 remainder 1 |
| 4 | 20 ÷ 1 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 199 | 2189 |
| 114 and 103 | 11742 |
| 144 and 11 | 1584 |
| 45 and 167 | 7515 |
| 61 and 163 | 9943 |