Least Common Multiple (LCM) of 53 and 133
The least common multiple (LCM) of 53 and 133 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 53 and 133?
First, calculate the GCD of 53 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 133 = 0 remainder 53 |
| 2 | 133 ÷ 53 = 2 remainder 27 |
| 3 | 53 ÷ 27 = 1 remainder 26 |
| 4 | 27 ÷ 26 = 1 remainder 1 |
| 5 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 197 | 15760 |
| 120 and 17 | 2040 |
| 70 and 144 | 5040 |
| 31 and 92 | 2852 |
| 98 and 89 | 8722 |