Least Common Multiple (LCM) of 83 and 67
The least common multiple (LCM) of 83 and 67 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 83 and 67?
First, calculate the GCD of 83 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 67 = 1 remainder 16 |
| 2 | 67 ÷ 16 = 4 remainder 3 |
| 3 | 16 ÷ 3 = 5 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 184 | 6808 |
| 199 and 109 | 21691 |
| 44 and 23 | 1012 |
| 129 and 14 | 1806 |
| 169 and 12 | 2028 |