Least Common Multiple (LCM) of 76 and 97
The least common multiple (LCM) of 76 and 97 is 7372.
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 76 and 97?
First, calculate the GCD of 76 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 97 = 0 remainder 76 |
| 2 | 97 ÷ 76 = 1 remainder 21 |
| 3 | 76 ÷ 21 = 3 remainder 13 |
| 4 | 21 ÷ 13 = 1 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 44 | 4620 |
| 14 and 46 | 322 |
| 57 and 106 | 6042 |
| 147 and 158 | 23226 |
| 163 and 194 | 31622 |