Least Common Multiple (LCM) of 99 and 155
The least common multiple (LCM) of 99 and 155 is 15345.
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 155?
First, calculate the GCD of 99 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 155 = 0 remainder 99 |
| 2 | 155 ÷ 99 = 1 remainder 56 |
| 3 | 99 ÷ 56 = 1 remainder 43 |
| 4 | 56 ÷ 43 = 1 remainder 13 |
| 5 | 43 ÷ 13 = 3 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 57 | 1425 |
| 58 and 171 | 9918 |
| 13 and 19 | 247 |
| 166 and 34 | 2822 |
| 174 and 90 | 2610 |