Least Common Multiple (LCM) of 39 and 133
The least common multiple (LCM) of 39 and 133 is 5187.
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 39 and 133?
First, calculate the GCD of 39 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 133 = 0 remainder 39 |
| 2 | 133 ÷ 39 = 3 remainder 16 |
| 3 | 39 ÷ 16 = 2 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 13 | 1872 |
| 69 and 82 | 5658 |
| 140 and 197 | 27580 |
| 74 and 63 | 4662 |
| 20 and 135 | 540 |