Least Common Multiple (LCM) of 133 and 170
The least common multiple (LCM) of 133 and 170 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 133 and 170?
First, calculate the GCD of 133 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 170 = 0 remainder 133 |
| 2 | 170 ÷ 133 = 1 remainder 37 |
| 3 | 133 ÷ 37 = 3 remainder 22 |
| 4 | 37 ÷ 22 = 1 remainder 15 |
| 5 | 22 ÷ 15 = 1 remainder 7 |
| 6 | 15 ÷ 7 = 2 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 178 | 178 |
| 50 and 172 | 4300 |
| 104 and 199 | 20696 |
| 94 and 112 | 5264 |
| 167 and 34 | 5678 |