Least Common Multiple (LCM) of 133 and 55
The least common multiple (LCM) of 133 and 55 is 7315.
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 55?
First, calculate the GCD of 133 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 55 = 2 remainder 23 |
| 2 | 55 ÷ 23 = 2 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 83 | 8051 |
| 43 and 29 | 1247 |
| 169 and 154 | 26026 |
| 145 and 98 | 14210 |
| 24 and 20 | 120 |