Least Common Multiple (LCM) of 54 and 83
The least common multiple (LCM) of 54 and 83 is 4482.
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 54 and 83?
First, calculate the GCD of 54 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 83 = 0 remainder 54 |
| 2 | 83 ÷ 54 = 1 remainder 29 |
| 3 | 54 ÷ 29 = 1 remainder 25 |
| 4 | 29 ÷ 25 = 1 remainder 4 |
| 5 | 25 ÷ 4 = 6 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 171 | 33174 |
| 75 and 157 | 11775 |
| 110 and 154 | 770 |
| 98 and 102 | 4998 |
| 39 and 60 | 780 |