Least Common Multiple (LCM) of 172 and 47
The least common multiple (LCM) of 172 and 47 is 8084.
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 47?
First, calculate the GCD of 172 and 47 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 47 = 3 remainder 31 |
| 2 | 47 ÷ 31 = 1 remainder 16 |
| 3 | 31 ÷ 16 = 1 remainder 15 |
| 4 | 16 ÷ 15 = 1 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 53 | 4346 |
| 109 and 57 | 6213 |
| 127 and 85 | 10795 |
| 108 and 30 | 540 |
| 24 and 75 | 600 |