Least Common Multiple (LCM) of 114 and 66
The least common multiple (LCM) of 114 and 66 is 1254.
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 114 and 66?
First, calculate the GCD of 114 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 66 = 1 remainder 48 |
| 2 | 66 ÷ 48 = 1 remainder 18 |
| 3 | 48 ÷ 18 = 2 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 53 | 9275 |
| 108 and 109 | 11772 |
| 167 and 111 | 18537 |
| 42 and 11 | 462 |
| 185 and 156 | 28860 |