Least Common Multiple (LCM) of 110 and 117
The least common multiple (LCM) of 110 and 117 is 12870.
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 110 and 117?
First, calculate the GCD of 110 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 117 = 0 remainder 110 |
| 2 | 117 ÷ 110 = 1 remainder 7 |
| 3 | 110 ÷ 7 = 15 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 70 | 5670 |
| 153 and 67 | 10251 |
| 141 and 90 | 4230 |
| 154 and 141 | 21714 |
| 199 and 44 | 8756 |