Least Common Multiple (LCM) of 67 and 69
The least common multiple (LCM) of 67 and 69 is 4623.
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 69?
First, calculate the GCD of 67 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 69 = 0 remainder 67 |
| 2 | 69 ÷ 67 = 1 remainder 2 |
| 3 | 67 ÷ 2 = 33 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 140 | 4340 |
| 33 and 34 | 1122 |
| 65 and 20 | 260 |
| 92 and 162 | 7452 |
| 109 and 42 | 4578 |