Least Common Multiple (LCM) of 106 and 154
The least common multiple (LCM) of 106 and 154 is 8162.
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 106 and 154?
First, calculate the GCD of 106 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 154 = 0 remainder 106 |
| 2 | 154 ÷ 106 = 1 remainder 48 |
| 3 | 106 ÷ 48 = 2 remainder 10 |
| 4 | 48 ÷ 10 = 4 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 41 | 7175 |
| 42 and 112 | 336 |
| 185 and 183 | 33855 |
| 110 and 51 | 5610 |
| 37 and 19 | 703 |