Least Common Multiple (LCM) of 105 and 12
The least common multiple (LCM) of 105 and 12 is 420.
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 12?
First, calculate the GCD of 105 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 12 = 8 remainder 9 |
| 2 | 12 ÷ 9 = 1 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 15 | 1830 |
| 154 and 151 | 23254 |
| 40 and 18 | 360 |
| 191 and 27 | 5157 |
| 119 and 164 | 19516 |