Least Common Multiple (LCM) of 47 and 172
The least common multiple (LCM) of 47 and 172 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 47 and 172?
First, calculate the GCD of 47 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 172 = 0 remainder 47 |
| 2 | 172 ÷ 47 = 3 remainder 31 |
| 3 | 47 ÷ 31 = 1 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 105 | 1785 |
| 115 and 171 | 19665 |
| 122 and 122 | 122 |
| 162 and 56 | 4536 |
| 69 and 67 | 4623 |