Least Common Multiple (LCM) of 75 and 133
The least common multiple (LCM) of 75 and 133 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 75 and 133?
First, calculate the GCD of 75 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 133 = 0 remainder 75 |
| 2 | 133 ÷ 75 = 1 remainder 58 |
| 3 | 75 ÷ 58 = 1 remainder 17 |
| 4 | 58 ÷ 17 = 3 remainder 7 |
| 5 | 17 ÷ 7 = 2 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 53 | 5565 |
| 135 and 96 | 4320 |
| 17 and 136 | 136 |
| 163 and 29 | 4727 |
| 155 and 20 | 620 |