Least Common Multiple (LCM) of 45 and 39
The least common multiple (LCM) of 45 and 39 is 585.
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 45 and 39?
First, calculate the GCD of 45 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 39 = 1 remainder 6 |
| 2 | 39 ÷ 6 = 6 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 36 | 6948 |
| 36 and 185 | 6660 |
| 134 and 101 | 13534 |
| 21 and 122 | 2562 |
| 108 and 28 | 756 |