Least Common Multiple (LCM) of 107 and 10
The least common multiple (LCM) of 107 and 10 is 1070.
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 107 and 10?
First, calculate the GCD of 107 and 10 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 10 = 10 remainder 7 |
| 2 | 10 ÷ 7 = 1 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 45 | 315 |
| 33 and 75 | 825 |
| 190 and 81 | 15390 |
| 49 and 84 | 588 |
| 167 and 196 | 32732 |