Least Common Multiple (LCM) of 117 and 110
The least common multiple (LCM) of 117 and 110 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 117 and 110?
First, calculate the GCD of 117 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 110 = 1 remainder 7 |
| 2 | 110 ÷ 7 = 15 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 110 | 4290 |
| 87 and 103 | 8961 |
| 194 and 87 | 16878 |
| 164 and 64 | 2624 |
| 192 and 117 | 7488 |