Least Common Multiple (LCM) of 67 and 80
The least common multiple (LCM) of 67 and 80 is 5360.
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 80?
First, calculate the GCD of 67 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 80 = 0 remainder 67 |
| 2 | 80 ÷ 67 = 1 remainder 13 |
| 3 | 67 ÷ 13 = 5 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 33 | 1551 |
| 44 and 39 | 1716 |
| 105 and 56 | 840 |
| 14 and 61 | 854 |
| 66 and 151 | 9966 |