Least Common Multiple (LCM) of 113 and 34
The least common multiple (LCM) of 113 and 34 is 3842.
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 34?
First, calculate the GCD of 113 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 34 = 3 remainder 11 |
| 2 | 34 ÷ 11 = 3 remainder 1 |
| 3 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 64 | 6976 |
| 169 and 187 | 31603 |
| 169 and 189 | 31941 |
| 38 and 24 | 456 |
| 67 and 77 | 5159 |