Least Common Multiple (LCM) of 66 and 100
The least common multiple (LCM) of 66 and 100 is 3300.
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 100?
First, calculate the GCD of 66 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 100 = 0 remainder 66 |
| 2 | 100 ÷ 66 = 1 remainder 34 |
| 3 | 66 ÷ 34 = 1 remainder 32 |
| 4 | 34 ÷ 32 = 1 remainder 2 |
| 5 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 15 | 1965 |
| 31 and 157 | 4867 |
| 102 and 39 | 1326 |
| 59 and 132 | 7788 |
| 193 and 91 | 17563 |