Least Common Multiple (LCM) of 113 and 72
The least common multiple (LCM) of 113 and 72 is 8136.
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 72?
First, calculate the GCD of 113 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 72 = 1 remainder 41 |
| 2 | 72 ÷ 41 = 1 remainder 31 |
| 3 | 41 ÷ 31 = 1 remainder 10 |
| 4 | 31 ÷ 10 = 3 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 19 | 3268 |
| 25 and 179 | 4475 |
| 80 and 191 | 15280 |
| 54 and 190 | 5130 |
| 111 and 35 | 3885 |