Least Common Multiple (LCM) of 133 and 71
The least common multiple (LCM) of 133 and 71 is 9443.
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 71?
First, calculate the GCD of 133 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 71 = 1 remainder 62 |
| 2 | 71 ÷ 62 = 1 remainder 9 |
| 3 | 62 ÷ 9 = 6 remainder 8 |
| 4 | 9 ÷ 8 = 1 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 70 | 13930 |
| 104 and 143 | 1144 |
| 142 and 125 | 17750 |
| 36 and 168 | 504 |
| 135 and 152 | 20520 |