Least Common Multiple (LCM) of 170 and 133
The least common multiple (LCM) of 170 and 133 is 22610.
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 133?
First, calculate the GCD of 170 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 133 = 1 remainder 37 |
| 2 | 133 ÷ 37 = 3 remainder 22 |
| 3 | 37 ÷ 22 = 1 remainder 15 |
| 4 | 22 ÷ 15 = 1 remainder 7 |
| 5 | 15 ÷ 7 = 2 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 48 | 48 |
| 103 and 137 | 14111 |
| 102 and 152 | 7752 |
| 16 and 162 | 1296 |
| 198 and 192 | 6336 |