Least Common Multiple (LCM) of 99 and 179
The least common multiple (LCM) of 99 and 179 is 17721.
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 179?
First, calculate the GCD of 99 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 179 = 0 remainder 99 |
| 2 | 179 ÷ 99 = 1 remainder 80 |
| 3 | 99 ÷ 80 = 1 remainder 19 |
| 4 | 80 ÷ 19 = 4 remainder 4 |
| 5 | 19 ÷ 4 = 4 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 135 | 11205 |
| 63 and 135 | 945 |
| 149 and 135 | 20115 |
| 54 and 122 | 3294 |
| 27 and 160 | 4320 |