Least Common Multiple (LCM) of 77 and 197
The least common multiple (LCM) of 77 and 197 is 15169.
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 77 and 197?
First, calculate the GCD of 77 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 197 = 0 remainder 77 |
| 2 | 197 ÷ 77 = 2 remainder 43 |
| 3 | 77 ÷ 43 = 1 remainder 34 |
| 4 | 43 ÷ 34 = 1 remainder 9 |
| 5 | 34 ÷ 9 = 3 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 165 | 2640 |
| 68 and 103 | 7004 |
| 122 and 53 | 6466 |
| 151 and 90 | 13590 |
| 119 and 106 | 12614 |