Least Common Multiple (LCM) of 10 and 116
The least common multiple (LCM) of 10 and 116 is 580.
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 116?
First, calculate the GCD of 10 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 116 = 0 remainder 10 |
| 2 | 116 ÷ 10 = 11 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 125 | 18250 |
| 66 and 49 | 3234 |
| 130 and 96 | 6240 |
| 166 and 60 | 4980 |
| 170 and 99 | 16830 |