Least Common Multiple (LCM) of 133 and 53
The least common multiple (LCM) of 133 and 53 is 7049.
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 53?
First, calculate the GCD of 133 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 53 = 2 remainder 27 |
| 2 | 53 ÷ 27 = 1 remainder 26 |
| 3 | 27 ÷ 26 = 1 remainder 1 |
| 4 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 57 | 2736 |
| 105 and 29 | 3045 |
| 145 and 53 | 7685 |
| 163 and 149 | 24287 |
| 76 and 167 | 12692 |