Least Common Multiple (LCM) of 67 and 109
The least common multiple (LCM) of 67 and 109 is 7303.
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 67 and 109?
First, calculate the GCD of 67 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 109 = 0 remainder 67 |
| 2 | 109 ÷ 67 = 1 remainder 42 |
| 3 | 67 ÷ 42 = 1 remainder 25 |
| 4 | 42 ÷ 25 = 1 remainder 17 |
| 5 | 25 ÷ 17 = 1 remainder 8 |
| 6 | 17 ÷ 8 = 2 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 39 | 1248 |
| 88 and 159 | 13992 |
| 112 and 142 | 7952 |
| 155 and 68 | 10540 |
| 100 and 29 | 2900 |