Least Common Multiple (LCM) of 113 and 32
The least common multiple (LCM) of 113 and 32 is 3616.
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 32?
First, calculate the GCD of 113 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 32 = 3 remainder 17 |
| 2 | 32 ÷ 17 = 1 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 37 | 37 |
| 59 and 78 | 4602 |
| 141 and 136 | 19176 |
| 111 and 174 | 6438 |
| 92 and 61 | 5612 |