Least Common Multiple (LCM) of 38 and 66
The least common multiple (LCM) of 38 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 38 and 66?
First, calculate the GCD of 38 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 38 ÷ 66 = 0 remainder 38 |
| 2 | 66 ÷ 38 = 1 remainder 28 |
| 3 | 38 ÷ 28 = 1 remainder 10 |
| 4 | 28 ÷ 10 = 2 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 146 | 5110 |
| 42 and 32 | 672 |
| 174 and 125 | 21750 |
| 134 and 35 | 4690 |
| 183 and 105 | 6405 |