Least Common Multiple (LCM) of 99 and 170
The least common multiple (LCM) of 99 and 170 is 16830.
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 170?
First, calculate the GCD of 99 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 170 = 0 remainder 99 |
| 2 | 170 ÷ 99 = 1 remainder 71 |
| 3 | 99 ÷ 71 = 1 remainder 28 |
| 4 | 71 ÷ 28 = 2 remainder 15 |
| 5 | 28 ÷ 15 = 1 remainder 13 |
| 6 | 15 ÷ 13 = 1 remainder 2 |
| 7 | 13 ÷ 2 = 6 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 69 | 7314 |
| 194 and 75 | 14550 |
| 91 and 117 | 819 |
| 174 and 176 | 15312 |
| 44 and 161 | 7084 |