Least Common Multiple (LCM) of 109 and 133
The least common multiple (LCM) of 109 and 133 is 14497.
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 109 and 133?
First, calculate the GCD of 109 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 133 = 0 remainder 109 |
| 2 | 133 ÷ 109 = 1 remainder 24 |
| 3 | 109 ÷ 24 = 4 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 134 | 6566 |
| 138 and 83 | 11454 |
| 171 and 155 | 26505 |
| 52 and 97 | 5044 |
| 119 and 180 | 21420 |