Least Common Multiple (LCM) of 66 and 108
The least common multiple (LCM) of 66 and 108 is 1188.
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 108?
First, calculate the GCD of 66 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 108 = 0 remainder 66 |
| 2 | 108 ÷ 66 = 1 remainder 42 |
| 3 | 66 ÷ 42 = 1 remainder 24 |
| 4 | 42 ÷ 24 = 1 remainder 18 |
| 5 | 24 ÷ 18 = 1 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 176 | 12496 |
| 108 and 112 | 3024 |
| 75 and 53 | 3975 |
| 150 and 65 | 1950 |
| 87 and 85 | 7395 |