Least Common Multiple (LCM) of 105 and 154
The least common multiple (LCM) of 105 and 154 is 2310.
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 105 and 154?
First, calculate the GCD of 105 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 154 = 0 remainder 105 |
| 2 | 154 ÷ 105 = 1 remainder 49 |
| 3 | 105 ÷ 49 = 2 remainder 7 |
| 4 | 49 ÷ 7 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 146 | 3066 |
| 55 and 44 | 220 |
| 15 and 175 | 525 |
| 149 and 147 | 21903 |
| 42 and 21 | 42 |