Least Common Multiple (LCM) of 78 and 110
The least common multiple (LCM) of 78 and 110 is 4290.
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 78 and 110?
First, calculate the GCD of 78 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 110 = 0 remainder 78 |
| 2 | 110 ÷ 78 = 1 remainder 32 |
| 3 | 78 ÷ 32 = 2 remainder 14 |
| 4 | 32 ÷ 14 = 2 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 59 | 1298 |
| 160 and 168 | 3360 |
| 190 and 159 | 30210 |
| 137 and 61 | 8357 |
| 187 and 109 | 20383 |