Least Common Multiple (LCM) of 172 and 66
The least common multiple (LCM) of 172 and 66 is 5676.
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 66?
First, calculate the GCD of 172 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 66 = 2 remainder 40 |
| 2 | 66 ÷ 40 = 1 remainder 26 |
| 3 | 40 ÷ 26 = 1 remainder 14 |
| 4 | 26 ÷ 14 = 1 remainder 12 |
| 5 | 14 ÷ 12 = 1 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 175 | 34825 |
| 56 and 192 | 1344 |
| 115 and 55 | 1265 |
| 128 and 150 | 9600 |
| 186 and 70 | 6510 |