Least Common Multiple (LCM) of 99 and 168
The least common multiple (LCM) of 99 and 168 is 5544.
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 99 and 168?
First, calculate the GCD of 99 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 168 = 0 remainder 99 |
| 2 | 168 ÷ 99 = 1 remainder 69 |
| 3 | 99 ÷ 69 = 1 remainder 30 |
| 4 | 69 ÷ 30 = 2 remainder 9 |
| 5 | 30 ÷ 9 = 3 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 80 | 880 |
| 78 and 65 | 390 |
| 178 and 98 | 8722 |
| 184 and 130 | 11960 |
| 161 and 10 | 1610 |