Least Common Multiple (LCM) of 113 and 74
The least common multiple (LCM) of 113 and 74 is 8362.
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 74?
First, calculate the GCD of 113 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 74 = 1 remainder 39 |
| 2 | 74 ÷ 39 = 1 remainder 35 |
| 3 | 39 ÷ 35 = 1 remainder 4 |
| 4 | 35 ÷ 4 = 8 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 23 | 1012 |
| 58 and 89 | 5162 |
| 184 and 70 | 6440 |
| 177 and 65 | 11505 |
| 49 and 146 | 7154 |