Least Common Multiple (LCM) of 109 and 67
The least common multiple (LCM) of 109 and 67 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 109 and 67?
First, calculate the GCD of 109 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 67 = 1 remainder 42 |
| 2 | 67 ÷ 42 = 1 remainder 25 |
| 3 | 42 ÷ 25 = 1 remainder 17 |
| 4 | 25 ÷ 17 = 1 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 132 | 6996 |
| 69 and 64 | 4416 |
| 170 and 74 | 6290 |
| 27 and 56 | 1512 |
| 110 and 135 | 2970 |