Least Common Multiple (LCM) of 99 and 146
The least common multiple (LCM) of 99 and 146 is 14454.
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 146?
First, calculate the GCD of 99 and 146 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 146 = 0 remainder 99 |
| 2 | 146 ÷ 99 = 1 remainder 47 |
| 3 | 99 ÷ 47 = 2 remainder 5 |
| 4 | 47 ÷ 5 = 9 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 97 | 3007 |
| 159 and 190 | 30210 |
| 80 and 28 | 560 |
| 71 and 115 | 8165 |
| 141 and 160 | 22560 |