Least Common Multiple (LCM) of 110 and 78
The least common multiple (LCM) of 110 and 78 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 110 and 78?
First, calculate the GCD of 110 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 78 = 1 remainder 32 |
| 2 | 78 ÷ 32 = 2 remainder 14 |
| 3 | 32 ÷ 14 = 2 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 124 | 620 |
| 137 and 30 | 4110 |
| 111 and 50 | 5550 |
| 161 and 18 | 2898 |
| 70 and 124 | 4340 |