Least Common Multiple (LCM) of 78 and 113
The least common multiple (LCM) of 78 and 113 is 8814.
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 113?
First, calculate the GCD of 78 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 113 = 0 remainder 78 |
| 2 | 113 ÷ 78 = 1 remainder 35 |
| 3 | 78 ÷ 35 = 2 remainder 8 |
| 4 | 35 ÷ 8 = 4 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 98 | 8526 |
| 118 and 57 | 6726 |
| 100 and 131 | 13100 |
| 158 and 135 | 21330 |
| 188 and 127 | 23876 |