Least Common Multiple (LCM) of 66 and 104
The least common multiple (LCM) of 66 and 104 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 66 and 104?
First, calculate the GCD of 66 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 104 = 0 remainder 66 |
| 2 | 104 ÷ 66 = 1 remainder 38 |
| 3 | 66 ÷ 38 = 1 remainder 28 |
| 4 | 38 ÷ 28 = 1 remainder 10 |
| 5 | 28 ÷ 10 = 2 remainder 8 |
| 6 | 10 ÷ 8 = 1 remainder 2 |
| 7 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 74 | 1924 |
| 175 and 199 | 34825 |
| 75 and 186 | 4650 |
| 164 and 157 | 25748 |
| 127 and 17 | 2159 |