Least Common Multiple (LCM) of 172 and 113
The least common multiple (LCM) of 172 and 113 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 172 and 113?
First, calculate the GCD of 172 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 113 = 1 remainder 59 |
| 2 | 113 ÷ 59 = 1 remainder 54 |
| 3 | 59 ÷ 54 = 1 remainder 5 |
| 4 | 54 ÷ 5 = 10 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 159 | 28302 |
| 96 and 165 | 5280 |
| 182 and 23 | 4186 |
| 151 and 13 | 1963 |
| 11 and 94 | 1034 |