Least Common Multiple (LCM) of 45 and 66
The least common multiple (LCM) of 45 and 66 is 990.
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 45 and 66?
First, calculate the GCD of 45 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 66 = 0 remainder 45 |
| 2 | 66 ÷ 45 = 1 remainder 21 |
| 3 | 45 ÷ 21 = 2 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 76 | 15124 |
| 135 and 192 | 8640 |
| 105 and 95 | 1995 |
| 66 and 24 | 264 |
| 91 and 123 | 11193 |