Least Common Multiple (LCM) of 133 and 113
The least common multiple (LCM) of 133 and 113 is 15029.
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 113?
First, calculate the GCD of 133 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 113 = 1 remainder 20 |
| 2 | 113 ÷ 20 = 5 remainder 13 |
| 3 | 20 ÷ 13 = 1 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 15 | 210 |
| 162 and 174 | 4698 |
| 83 and 163 | 13529 |
| 24 and 151 | 3624 |
| 140 and 105 | 420 |