Least Common Multiple (LCM) of 53 and 82
The least common multiple (LCM) of 53 and 82 is 4346.
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 82?
First, calculate the GCD of 53 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 82 = 0 remainder 53 |
| 2 | 82 ÷ 53 = 1 remainder 29 |
| 3 | 53 ÷ 29 = 1 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 24 | 2760 |
| 149 and 146 | 21754 |
| 74 and 147 | 10878 |
| 174 and 108 | 3132 |
| 187 and 108 | 20196 |