Least Common Multiple (LCM) of 109 and 154
The least common multiple (LCM) of 109 and 154 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 109 and 154?
First, calculate the GCD of 109 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 154 = 0 remainder 109 |
| 2 | 154 ÷ 109 = 1 remainder 45 |
| 3 | 109 ÷ 45 = 2 remainder 19 |
| 4 | 45 ÷ 19 = 2 remainder 7 |
| 5 | 19 ÷ 7 = 2 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 60 | 2820 |
| 167 and 136 | 22712 |
| 120 and 75 | 600 |
| 101 and 96 | 9696 |
| 157 and 157 | 157 |