Least Common Multiple (LCM) of 133 and 75
The least common multiple (LCM) of 133 and 75 is 9975.
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 75?
First, calculate the GCD of 133 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 75 = 1 remainder 58 |
| 2 | 75 ÷ 58 = 1 remainder 17 |
| 3 | 58 ÷ 17 = 3 remainder 7 |
| 4 | 17 ÷ 7 = 2 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 97 | 3104 |
| 140 and 21 | 420 |
| 111 and 42 | 1554 |
| 50 and 36 | 900 |
| 24 and 162 | 648 |