Least Common Multiple (LCM) of 133 and 69
The least common multiple (LCM) of 133 and 69 is 9177.
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 69?
First, calculate the GCD of 133 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 69 = 1 remainder 64 |
| 2 | 69 ÷ 64 = 1 remainder 5 |
| 3 | 64 ÷ 5 = 12 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 102 | 2244 |
| 92 and 59 | 5428 |
| 176 and 86 | 7568 |
| 175 and 179 | 31325 |
| 13 and 45 | 585 |