Least Common Multiple (LCM) of 97 and 45
The least common multiple (LCM) of 97 and 45 is 4365.
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 45?
First, calculate the GCD of 97 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 45 = 2 remainder 7 |
| 2 | 45 ÷ 7 = 6 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 49 | 5635 |
| 161 and 186 | 29946 |
| 57 and 132 | 2508 |
| 53 and 21 | 1113 |
| 42 and 193 | 8106 |