Least Common Multiple (LCM) of 104 and 66
The least common multiple (LCM) of 104 and 66 is 3432.
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 104 and 66?
First, calculate the GCD of 104 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 66 = 1 remainder 38 |
| 2 | 66 ÷ 38 = 1 remainder 28 |
| 3 | 38 ÷ 28 = 1 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 161 | 25277 |
| 114 and 92 | 5244 |
| 90 and 24 | 360 |
| 148 and 20 | 740 |
| 198 and 45 | 990 |