Least Common Multiple (LCM) of 113 and 178
The least common multiple (LCM) of 113 and 178 is 20114.
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 178?
First, calculate the GCD of 113 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 178 = 0 remainder 113 |
| 2 | 178 ÷ 113 = 1 remainder 65 |
| 3 | 113 ÷ 65 = 1 remainder 48 |
| 4 | 65 ÷ 48 = 1 remainder 17 |
| 5 | 48 ÷ 17 = 2 remainder 14 |
| 6 | 17 ÷ 14 = 1 remainder 3 |
| 7 | 14 ÷ 3 = 4 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 157 | 16485 |
| 117 and 174 | 6786 |
| 51 and 67 | 3417 |
| 169 and 125 | 21125 |
| 56 and 162 | 4536 |