Least Common Multiple (LCM) of 49 and 82
The least common multiple (LCM) of 49 and 82 is 4018.
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 49 and 82?
First, calculate the GCD of 49 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 82 = 0 remainder 49 |
| 2 | 82 ÷ 49 = 1 remainder 33 |
| 3 | 49 ÷ 33 = 1 remainder 16 |
| 4 | 33 ÷ 16 = 2 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 13 | 936 |
| 92 and 106 | 4876 |
| 190 and 102 | 9690 |
| 99 and 45 | 495 |
| 72 and 83 | 5976 |