Least Common Multiple (LCM) of 133 and 97
The least common multiple (LCM) of 133 and 97 is 12901.
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 97?
First, calculate the GCD of 133 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 97 = 1 remainder 36 |
| 2 | 97 ÷ 36 = 2 remainder 25 |
| 3 | 36 ÷ 25 = 1 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 162 | 5670 |
| 65 and 92 | 5980 |
| 17 and 60 | 1020 |
| 187 and 144 | 26928 |
| 82 and 37 | 3034 |