Least Common Multiple (LCM) of 84 and 99
The least common multiple (LCM) of 84 and 99 is 2772.
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 99?
First, calculate the GCD of 84 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 99 = 0 remainder 84 |
| 2 | 99 ÷ 84 = 1 remainder 15 |
| 3 | 84 ÷ 15 = 5 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 104 | 2392 |
| 114 and 163 | 18582 |
| 173 and 36 | 6228 |
| 25 and 45 | 225 |
| 133 and 112 | 2128 |