Least Common Multiple (LCM) of 17 and 66
The least common multiple (LCM) of 17 and 66 is 1122.
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 17 and 66?
First, calculate the GCD of 17 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 17 ÷ 66 = 0 remainder 17 |
| 2 | 66 ÷ 17 = 3 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 32 | 3808 |
| 35 and 117 | 4095 |
| 73 and 106 | 7738 |
| 123 and 25 | 3075 |
| 132 and 165 | 660 |