Least Common Multiple (LCM) of 172 and 133
The least common multiple (LCM) of 172 and 133 is 22876.
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 172 and 133?
First, calculate the GCD of 172 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 133 = 1 remainder 39 |
| 2 | 133 ÷ 39 = 3 remainder 16 |
| 3 | 39 ÷ 16 = 2 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 103 | 5871 |
| 68 and 170 | 340 |
| 142 and 90 | 6390 |
| 54 and 120 | 1080 |
| 49 and 192 | 9408 |