Least Common Multiple (LCM) of 76 and 83
The least common multiple (LCM) of 76 and 83 is 6308.
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 76 and 83?
First, calculate the GCD of 76 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 83 = 0 remainder 76 |
| 2 | 83 ÷ 76 = 1 remainder 7 |
| 3 | 76 ÷ 7 = 10 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 55 | 9570 |
| 43 and 166 | 7138 |
| 123 and 173 | 21279 |
| 184 and 17 | 3128 |
| 21 and 153 | 1071 |