Least Common Multiple (LCM) of 66 and 172
The least common multiple (LCM) of 66 and 172 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 66 and 172?
First, calculate the GCD of 66 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 172 = 0 remainder 66 |
| 2 | 172 ÷ 66 = 2 remainder 40 |
| 3 | 66 ÷ 40 = 1 remainder 26 |
| 4 | 40 ÷ 26 = 1 remainder 14 |
| 5 | 26 ÷ 14 = 1 remainder 12 |
| 6 | 14 ÷ 12 = 1 remainder 2 |
| 7 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 183 | 34953 |
| 68 and 42 | 1428 |
| 136 and 161 | 21896 |
| 105 and 200 | 4200 |
| 44 and 11 | 44 |