Least Common Multiple (LCM) of 105 and 189
The least common multiple (LCM) of 105 and 189 is 945.
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 189?
First, calculate the GCD of 105 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 189 = 0 remainder 105 |
| 2 | 189 ÷ 105 = 1 remainder 84 |
| 3 | 105 ÷ 84 = 1 remainder 21 |
| 4 | 84 ÷ 21 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 143 | 23881 |
| 100 and 145 | 2900 |
| 111 and 131 | 14541 |
| 86 and 98 | 4214 |
| 172 and 179 | 30788 |