Least Common Multiple (LCM) of 133 and 52
The least common multiple (LCM) of 133 and 52 is 6916.
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 52?
First, calculate the GCD of 133 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 52 = 2 remainder 29 |
| 2 | 52 ÷ 29 = 1 remainder 23 |
| 3 | 29 ÷ 23 = 1 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 132 | 660 |
| 67 and 185 | 12395 |
| 113 and 38 | 4294 |
| 196 and 37 | 7252 |
| 131 and 153 | 20043 |