Least Common Multiple (LCM) of 27 and 84
The least common multiple (LCM) of 27 and 84 is 756.
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 27 and 84?
First, calculate the GCD of 27 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 84 = 0 remainder 27 |
| 2 | 84 ÷ 27 = 3 remainder 3 |
| 3 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 25 | 275 |
| 199 and 21 | 4179 |
| 12 and 41 | 492 |
| 172 and 51 | 8772 |
| 46 and 145 | 6670 |