Least Common Multiple (LCM) of 154 and 109
The least common multiple (LCM) of 154 and 109 is 16786.
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 154 and 109?
First, calculate the GCD of 154 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 109 = 1 remainder 45 |
| 2 | 109 ÷ 45 = 2 remainder 19 |
| 3 | 45 ÷ 19 = 2 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 183 | 9150 |
| 53 and 140 | 7420 |
| 189 and 181 | 34209 |
| 96 and 30 | 480 |
| 109 and 120 | 13080 |