Least Common Multiple (LCM) of 83 and 53
The least common multiple (LCM) of 83 and 53 is 4399.
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 83 and 53?
First, calculate the GCD of 83 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 53 = 1 remainder 30 |
| 2 | 53 ÷ 30 = 1 remainder 23 |
| 3 | 30 ÷ 23 = 1 remainder 7 |
| 4 | 23 ÷ 7 = 3 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 163 | 17930 |
| 83 and 188 | 15604 |
| 149 and 132 | 19668 |
| 154 and 92 | 7084 |
| 177 and 200 | 35400 |