Least Common Multiple (LCM) of 67 and 83
The least common multiple (LCM) of 67 and 83 is 5561.
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 67 and 83?
First, calculate the GCD of 67 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 83 = 0 remainder 67 |
| 2 | 83 ÷ 67 = 1 remainder 16 |
| 3 | 67 ÷ 16 = 4 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 77 | 14784 |
| 166 and 11 | 1826 |
| 174 and 15 | 870 |
| 92 and 97 | 8924 |
| 49 and 128 | 6272 |