Least Common Multiple (LCM) of 53 and 83
The least common multiple (LCM) of 53 and 83 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 53 and 83?
First, calculate the GCD of 53 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 83 = 0 remainder 53 |
| 2 | 83 ÷ 53 = 1 remainder 30 |
| 3 | 53 ÷ 30 = 1 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 147 | 25872 |
| 62 and 18 | 558 |
| 56 and 20 | 280 |
| 91 and 166 | 15106 |
| 66 and 72 | 792 |