Least Common Multiple (LCM) of 84 and 39
The least common multiple (LCM) of 84 and 39 is 1092.
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 84 and 39?
First, calculate the GCD of 84 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 39 = 2 remainder 6 |
| 2 | 39 ÷ 6 = 6 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 105 | 1155 |
| 18 and 135 | 270 |
| 193 and 73 | 14089 |
| 119 and 105 | 1785 |
| 135 and 15 | 135 |