Least Common Multiple (LCM) of 133 and 174
The least common multiple (LCM) of 133 and 174 is 23142.
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 174?
First, calculate the GCD of 133 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 174 = 0 remainder 133 |
| 2 | 174 ÷ 133 = 1 remainder 41 |
| 3 | 133 ÷ 41 = 3 remainder 10 |
| 4 | 41 ÷ 10 = 4 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 37 | 1406 |
| 120 and 104 | 1560 |
| 188 and 117 | 21996 |
| 13 and 196 | 2548 |
| 135 and 192 | 8640 |