Least Common Multiple (LCM) of 105 and 10
The least common multiple (LCM) of 105 and 10 is 210.
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 10?
First, calculate the GCD of 105 and 10 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 10 = 10 remainder 5 |
| 2 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 68 | 9180 |
| 164 and 82 | 164 |
| 150 and 124 | 9300 |
| 18 and 95 | 1710 |
| 188 and 71 | 13348 |