Least Common Multiple (LCM) of 97 and 77
The least common multiple (LCM) of 97 and 77 is 7469.
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 97 and 77?
First, calculate the GCD of 97 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 77 = 1 remainder 20 |
| 2 | 77 ÷ 20 = 3 remainder 17 |
| 3 | 20 ÷ 17 = 1 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 146 | 23214 |
| 59 and 44 | 2596 |
| 113 and 58 | 6554 |
| 105 and 67 | 7035 |
| 59 and 36 | 2124 |