Least Common Multiple (LCM) of 72 and 173
The least common multiple (LCM) of 72 and 173 is 12456.
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 72 and 173?
First, calculate the GCD of 72 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 173 = 0 remainder 72 |
| 2 | 173 ÷ 72 = 2 remainder 29 |
| 3 | 72 ÷ 29 = 2 remainder 14 |
| 4 | 29 ÷ 14 = 2 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 143 | 17589 |
| 85 and 76 | 6460 |
| 193 and 125 | 24125 |
| 75 and 80 | 1200 |
| 40 and 42 | 840 |