Least Common Multiple (LCM) of 52 and 82
The least common multiple (LCM) of 52 and 82 is 2132.
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 52 and 82?
First, calculate the GCD of 52 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 82 = 0 remainder 52 |
| 2 | 82 ÷ 52 = 1 remainder 30 |
| 3 | 52 ÷ 30 = 1 remainder 22 |
| 4 | 30 ÷ 22 = 1 remainder 8 |
| 5 | 22 ÷ 8 = 2 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 37 | 2516 |
| 127 and 45 | 5715 |
| 172 and 25 | 4300 |
| 154 and 45 | 6930 |
| 145 and 107 | 15515 |