Least Common Multiple (LCM) of 84 and 27
The least common multiple (LCM) of 84 and 27 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 84 and 27?
First, calculate the GCD of 84 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 27 = 3 remainder 3 |
| 2 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 168 | 3864 |
| 135 and 123 | 5535 |
| 77 and 159 | 12243 |
| 153 and 189 | 3213 |
| 23 and 168 | 3864 |