Least Common Multiple (LCM) of 24 and 83
The least common multiple (LCM) of 24 and 83 is 1992.
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 24 and 83?
First, calculate the GCD of 24 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 24 ÷ 83 = 0 remainder 24 |
| 2 | 83 ÷ 24 = 3 remainder 11 |
| 3 | 24 ÷ 11 = 2 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 110 | 14630 |
| 198 and 188 | 18612 |
| 34 and 127 | 4318 |
| 72 and 36 | 72 |
| 123 and 33 | 1353 |