Least Common Multiple (LCM) of 66 and 25
The least common multiple (LCM) of 66 and 25 is 1650.
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 25?
First, calculate the GCD of 66 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 25 = 2 remainder 16 |
| 2 | 25 ÷ 16 = 1 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 11 | 1606 |
| 142 and 29 | 4118 |
| 193 and 153 | 29529 |
| 184 and 137 | 25208 |
| 66 and 65 | 4290 |