Least Common Multiple (LCM) of 83 and 74
The least common multiple (LCM) of 83 and 74 is 6142.
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 74?
First, calculate the GCD of 83 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 74 = 1 remainder 9 |
| 2 | 74 ÷ 9 = 8 remainder 2 |
| 3 | 9 ÷ 2 = 4 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 110 | 13530 |
| 14 and 76 | 532 |
| 154 and 105 | 2310 |
| 42 and 30 | 210 |
| 116 and 110 | 6380 |