Least Common Multiple (LCM) of 99 and 149
The least common multiple (LCM) of 99 and 149 is 14751.
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 149?
First, calculate the GCD of 99 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 149 = 0 remainder 99 |
| 2 | 149 ÷ 99 = 1 remainder 50 |
| 3 | 99 ÷ 50 = 1 remainder 49 |
| 4 | 50 ÷ 49 = 1 remainder 1 |
| 5 | 49 ÷ 1 = 49 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 76 | 14820 |
| 47 and 191 | 8977 |
| 45 and 171 | 855 |
| 199 and 71 | 14129 |
| 177 and 97 | 17169 |