Least Common Multiple (LCM) of 66 and 118
The least common multiple (LCM) of 66 and 118 is 3894.
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 118?
First, calculate the GCD of 66 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 118 = 0 remainder 66 |
| 2 | 118 ÷ 66 = 1 remainder 52 |
| 3 | 66 ÷ 52 = 1 remainder 14 |
| 4 | 52 ÷ 14 = 3 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 53 | 4452 |
| 75 and 169 | 12675 |
| 31 and 103 | 3193 |
| 106 and 19 | 2014 |
| 32 and 55 | 1760 |