Least Common Multiple (LCM) of 117 and 133
The least common multiple (LCM) of 117 and 133 is 15561.
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 117 and 133?
First, calculate the GCD of 117 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 133 = 0 remainder 117 |
| 2 | 133 ÷ 117 = 1 remainder 16 |
| 3 | 117 ÷ 16 = 7 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 138 | 2622 |
| 135 and 57 | 2565 |
| 177 and 66 | 3894 |
| 21 and 115 | 2415 |
| 32 and 34 | 544 |