Least Common Multiple (LCM) of 99 and 177
The least common multiple (LCM) of 99 and 177 is 5841.
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 177?
First, calculate the GCD of 99 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 177 = 0 remainder 99 |
| 2 | 177 ÷ 99 = 1 remainder 78 |
| 3 | 99 ÷ 78 = 1 remainder 21 |
| 4 | 78 ÷ 21 = 3 remainder 15 |
| 5 | 21 ÷ 15 = 1 remainder 6 |
| 6 | 15 ÷ 6 = 2 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 21 | 2877 |
| 185 and 63 | 11655 |
| 29 and 25 | 725 |
| 80 and 196 | 3920 |
| 115 and 54 | 6210 |