Least Common Multiple (LCM) of 99 and 162
The least common multiple (LCM) of 99 and 162 is 1782.
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 162?
First, calculate the GCD of 99 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 162 = 0 remainder 99 |
| 2 | 162 ÷ 99 = 1 remainder 63 |
| 3 | 99 ÷ 63 = 1 remainder 36 |
| 4 | 63 ÷ 36 = 1 remainder 27 |
| 5 | 36 ÷ 27 = 1 remainder 9 |
| 6 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 55 | 10395 |
| 192 and 85 | 16320 |
| 135 and 120 | 1080 |
| 154 and 131 | 20174 |
| 42 and 191 | 8022 |