Least Common Multiple (LCM) of 10 and 105
The least common multiple (LCM) of 10 and 105 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 10 and 105?
First, calculate the GCD of 10 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 105 = 0 remainder 10 |
| 2 | 105 ÷ 10 = 10 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 91 | 8372 |
| 153 and 56 | 8568 |
| 192 and 88 | 2112 |
| 174 and 163 | 28362 |
| 96 and 134 | 6432 |