Least Common Multiple (LCM) of 113 and 78
The least common multiple (LCM) of 113 and 78 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 113 and 78?
First, calculate the GCD of 113 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 78 = 1 remainder 35 |
| 2 | 78 ÷ 35 = 2 remainder 8 |
| 3 | 35 ÷ 8 = 4 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 107 | 11770 |
| 164 and 156 | 6396 |
| 178 and 130 | 11570 |
| 77 and 25 | 1925 |
| 47 and 107 | 5029 |