Least Common Multiple (LCM) of 133 and 141
The least common multiple (LCM) of 133 and 141 is 18753.
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 141?
First, calculate the GCD of 133 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 141 = 0 remainder 133 |
| 2 | 141 ÷ 133 = 1 remainder 8 |
| 3 | 133 ÷ 8 = 16 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 12 | 84 |
| 14 and 181 | 2534 |
| 137 and 94 | 12878 |
| 20 and 112 | 560 |
| 114 and 76 | 228 |