Least Common Multiple (LCM) of 110 and 197
The least common multiple (LCM) of 110 and 197 is 21670.
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 197?
First, calculate the GCD of 110 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 197 = 0 remainder 110 |
| 2 | 197 ÷ 110 = 1 remainder 87 |
| 3 | 110 ÷ 87 = 1 remainder 23 |
| 4 | 87 ÷ 23 = 3 remainder 18 |
| 5 | 23 ÷ 18 = 1 remainder 5 |
| 6 | 18 ÷ 5 = 3 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 81 | 3321 |
| 39 and 31 | 1209 |
| 178 and 178 | 178 |
| 73 and 42 | 3066 |
| 108 and 16 | 432 |