Least Common Multiple (LCM) of 113 and 172
The least common multiple (LCM) of 113 and 172 is 19436.
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 172?
First, calculate the GCD of 113 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 172 = 0 remainder 113 |
| 2 | 172 ÷ 113 = 1 remainder 59 |
| 3 | 113 ÷ 59 = 1 remainder 54 |
| 4 | 59 ÷ 54 = 1 remainder 5 |
| 5 | 54 ÷ 5 = 10 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 11 | 143 |
| 190 and 98 | 9310 |
| 166 and 82 | 6806 |
| 195 and 106 | 20670 |
| 55 and 172 | 9460 |