Least Common Multiple (LCM) of 66 and 138
The least common multiple (LCM) of 66 and 138 is 1518.
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 138?
First, calculate the GCD of 66 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 138 = 0 remainder 66 |
| 2 | 138 ÷ 66 = 2 remainder 6 |
| 3 | 66 ÷ 6 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 108 | 3996 |
| 12 and 18 | 36 |
| 58 and 23 | 1334 |
| 105 and 65 | 1365 |
| 100 and 92 | 2300 |