Least Common Multiple (LCM) of 110 and 133
The least common multiple (LCM) of 110 and 133 is 14630.
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 110 and 133?
First, calculate the GCD of 110 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 133 = 0 remainder 110 |
| 2 | 133 ÷ 110 = 1 remainder 23 |
| 3 | 110 ÷ 23 = 4 remainder 18 |
| 4 | 23 ÷ 18 = 1 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 180 | 720 |
| 93 and 162 | 5022 |
| 33 and 78 | 858 |
| 125 and 80 | 2000 |
| 89 and 80 | 7120 |