Least Common Multiple (LCM) of 133 and 172
The least common multiple (LCM) of 133 and 172 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 133 and 172?
First, calculate the GCD of 133 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 172 = 0 remainder 133 |
| 2 | 172 ÷ 133 = 1 remainder 39 |
| 3 | 133 ÷ 39 = 3 remainder 16 |
| 4 | 39 ÷ 16 = 2 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 164 | 32636 |
| 110 and 194 | 10670 |
| 33 and 70 | 2310 |
| 101 and 139 | 14039 |
| 57 and 176 | 10032 |