Least Common Multiple (LCM) of 109 and 66
The least common multiple (LCM) of 109 and 66 is 7194.
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 109 and 66?
First, calculate the GCD of 109 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 66 = 1 remainder 43 |
| 2 | 66 ÷ 43 = 1 remainder 23 |
| 3 | 43 ÷ 23 = 1 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 163 | 21842 |
| 122 and 185 | 22570 |
| 112 and 65 | 7280 |
| 117 and 109 | 12753 |
| 19 and 136 | 2584 |