Least Common Multiple (LCM) of 197 and 76
The least common multiple (LCM) of 197 and 76 is 14972.
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 197 and 76?
First, calculate the GCD of 197 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 76 = 2 remainder 45 |
| 2 | 76 ÷ 45 = 1 remainder 31 |
| 3 | 45 ÷ 31 = 1 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 70 | 2520 |
| 24 and 116 | 696 |
| 109 and 95 | 10355 |
| 169 and 165 | 27885 |
| 91 and 102 | 9282 |