Least Common Multiple (LCM) of 84 and 111
The least common multiple (LCM) of 84 and 111 is 3108.
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 111?
First, calculate the GCD of 84 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 111 = 0 remainder 84 |
| 2 | 111 ÷ 84 = 1 remainder 27 |
| 3 | 84 ÷ 27 = 3 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 116 | 1276 |
| 33 and 71 | 2343 |
| 112 and 67 | 7504 |
| 162 and 174 | 4698 |
| 76 and 89 | 6764 |