Least Common Multiple (LCM) of 45 and 133
The least common multiple (LCM) of 45 and 133 is 5985.
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 45 and 133?
First, calculate the GCD of 45 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 133 = 0 remainder 45 |
| 2 | 133 ÷ 45 = 2 remainder 43 |
| 3 | 45 ÷ 43 = 1 remainder 2 |
| 4 | 43 ÷ 2 = 21 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 197 | 27974 |
| 105 and 62 | 6510 |
| 124 and 79 | 9796 |
| 112 and 175 | 2800 |
| 160 and 189 | 30240 |