Least Common Multiple (LCM) of 80 and 97
The least common multiple (LCM) of 80 and 97 is 7760.
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 80 and 97?
First, calculate the GCD of 80 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 97 = 0 remainder 80 |
| 2 | 97 ÷ 80 = 1 remainder 17 |
| 3 | 80 ÷ 17 = 4 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 111 | 17760 |
| 71 and 109 | 7739 |
| 102 and 164 | 8364 |
| 27 and 77 | 2079 |
| 86 and 35 | 3010 |