Least Common Multiple (LCM) of 111 and 84
The least common multiple (LCM) of 111 and 84 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 111 and 84?
First, calculate the GCD of 111 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 84 = 1 remainder 27 |
| 2 | 84 ÷ 27 = 3 remainder 3 |
| 3 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 195 | 10335 |
| 143 and 13 | 143 |
| 138 and 29 | 4002 |
| 97 and 113 | 10961 |
| 83 and 96 | 7968 |