Least Common Multiple (LCM) of 113 and 174
The least common multiple (LCM) of 113 and 174 is 19662.
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 174?
First, calculate the GCD of 113 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 174 = 0 remainder 113 |
| 2 | 174 ÷ 113 = 1 remainder 61 |
| 3 | 113 ÷ 61 = 1 remainder 52 |
| 4 | 61 ÷ 52 = 1 remainder 9 |
| 5 | 52 ÷ 9 = 5 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 135 | 20115 |
| 11 and 100 | 1100 |
| 39 and 184 | 7176 |
| 54 and 55 | 2970 |
| 117 and 131 | 15327 |