Least Common Multiple (LCM) of 18 and 84
The least common multiple (LCM) of 18 and 84 is 252.
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 18 and 84?
First, calculate the GCD of 18 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 84 = 0 remainder 18 |
| 2 | 84 ÷ 18 = 4 remainder 12 |
| 3 | 18 ÷ 12 = 1 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 146 | 15330 |
| 136 and 152 | 2584 |
| 149 and 151 | 22499 |
| 100 and 113 | 11300 |
| 71 and 14 | 994 |