Least Common Multiple (LCM) of 66 and 167
The least common multiple (LCM) of 66 and 167 is 11022.
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 167?
First, calculate the GCD of 66 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 167 = 0 remainder 66 |
| 2 | 167 ÷ 66 = 2 remainder 35 |
| 3 | 66 ÷ 35 = 1 remainder 31 |
| 4 | 35 ÷ 31 = 1 remainder 4 |
| 5 | 31 ÷ 4 = 7 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 65 | 2145 |
| 185 and 144 | 26640 |
| 192 and 191 | 36672 |
| 154 and 27 | 4158 |
| 187 and 94 | 17578 |