Least Common Multiple (LCM) of 99 and 134
The least common multiple (LCM) of 99 and 134 is 13266.
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 134?
First, calculate the GCD of 99 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 134 = 0 remainder 99 |
| 2 | 134 ÷ 99 = 1 remainder 35 |
| 3 | 99 ÷ 35 = 2 remainder 29 |
| 4 | 35 ÷ 29 = 1 remainder 6 |
| 5 | 29 ÷ 6 = 4 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 159 | 318 |
| 129 and 102 | 4386 |
| 10 and 185 | 370 |
| 107 and 174 | 18618 |
| 59 and 109 | 6431 |