Least Common Multiple (LCM) of 170 and 99
The least common multiple (LCM) of 170 and 99 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 170 and 99?
First, calculate the GCD of 170 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 99 = 1 remainder 71 |
| 2 | 99 ÷ 71 = 1 remainder 28 |
| 3 | 71 ÷ 28 = 2 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 173 | 21106 |
| 118 and 124 | 7316 |
| 122 and 51 | 6222 |
| 79 and 145 | 11455 |
| 185 and 39 | 7215 |