Least Common Multiple (LCM) of 99 and 135
The least common multiple (LCM) of 99 and 135 is 1485.
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 135?
First, calculate the GCD of 99 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 135 = 0 remainder 99 |
| 2 | 135 ÷ 99 = 1 remainder 36 |
| 3 | 99 ÷ 36 = 2 remainder 27 |
| 4 | 36 ÷ 27 = 1 remainder 9 |
| 5 | 27 ÷ 9 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 35 | 455 |
| 183 and 109 | 19947 |
| 67 and 126 | 8442 |
| 176 and 130 | 11440 |
| 189 and 167 | 31563 |