Least Common Multiple (LCM) of 110 and 196
The least common multiple (LCM) of 110 and 196 is 10780.
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 196?
First, calculate the GCD of 110 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 196 = 0 remainder 110 |
| 2 | 196 ÷ 110 = 1 remainder 86 |
| 3 | 110 ÷ 86 = 1 remainder 24 |
| 4 | 86 ÷ 24 = 3 remainder 14 |
| 5 | 24 ÷ 14 = 1 remainder 10 |
| 6 | 14 ÷ 10 = 1 remainder 4 |
| 7 | 10 ÷ 4 = 2 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 139 | 23769 |
| 128 and 79 | 10112 |
| 51 and 83 | 4233 |
| 41 and 176 | 7216 |
| 168 and 151 | 25368 |