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 |
|---|---|
| 107 and 165 | 17655 |
| 93 and 100 | 9300 |
| 81 and 103 | 8343 |
| 112 and 178 | 9968 |
| 107 and 151 | 16157 |