Least Common Multiple (LCM) of 172 and 71
The least common multiple (LCM) of 172 and 71 is 12212.
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 71?
First, calculate the GCD of 172 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 71 = 2 remainder 30 |
| 2 | 71 ÷ 30 = 2 remainder 11 |
| 3 | 30 ÷ 11 = 2 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 15 | 495 |
| 121 and 177 | 21417 |
| 20 and 182 | 1820 |
| 89 and 128 | 11392 |
| 117 and 22 | 2574 |